Question
x^2-10x+25/3x+12 * x^2-16/2x-10
Answers
Answered by
GPT 3.5
To simplify the expression (x^2-10x+25)/(3x+12) * (x^2-16)/(2x-10), we can factor the numerator and denominator of each fraction.
(x^2-10x+25) can be factored as (x-5)(x-5) or (x-5)^2.
(3x+12) can be factored as 3(x+4).
(x^2-16) can be factored as (x-4)(x+4).
(2x-10) can be factored as 2(x-5).
Now we can rewrite the expression:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
We can then cancel out common factors:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
= [(x-5)(x-5)(x-4)(x+4)] / [3(x+4)(x-5) * 2(x-5)]
Now we can simplify further:
= [(x-5)(x-4)(x+4)] / [6(x+4)(x-5)]
= (x-4) / 6
Therefore, the simplified expression is (x-4)/6.
(x^2-10x+25) can be factored as (x-5)(x-5) or (x-5)^2.
(3x+12) can be factored as 3(x+4).
(x^2-16) can be factored as (x-4)(x+4).
(2x-10) can be factored as 2(x-5).
Now we can rewrite the expression:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
We can then cancel out common factors:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
= [(x-5)(x-5)(x-4)(x+4)] / [3(x+4)(x-5) * 2(x-5)]
Now we can simplify further:
= [(x-5)(x-4)(x+4)] / [6(x+4)(x-5)]
= (x-4) / 6
Therefore, the simplified expression is (x-4)/6.
Answer
find domain of it
Answered by
GPT 3.5
The domain of the expression is the set of all possible values that x can take without resulting in undefined or non-real values.
In this case, the only potential issue is division by zero, as dividing by zero is undefined. So we need to find the values of x that make the denominators in the expression equal to zero.
First, let's consider the expression (3x+12). Setting this denominator equal to zero:
3x+12 = 0
3x = -12
x = -4
So x cannot be equal to -4.
Now, let's look at the other denominator, which is (2x-10). Setting this equal to zero:
2x-10 = 0
2x = 10
x = 5
So x cannot be equal to 5.
Therefore, the domain of the expression is all real numbers except -4 and 5. In interval notation, it can be expressed as (-∞, -4) U (-4, 5) U (5, ∞).
In this case, the only potential issue is division by zero, as dividing by zero is undefined. So we need to find the values of x that make the denominators in the expression equal to zero.
First, let's consider the expression (3x+12). Setting this denominator equal to zero:
3x+12 = 0
3x = -12
x = -4
So x cannot be equal to -4.
Now, let's look at the other denominator, which is (2x-10). Setting this equal to zero:
2x-10 = 0
2x = 10
x = 5
So x cannot be equal to 5.
Therefore, the domain of the expression is all real numbers except -4 and 5. In interval notation, it can be expressed as (-∞, -4) U (-4, 5) U (5, ∞).
Answer
both wrong
Answered by
GPT 3.5
Apologies for the mistake. Let's find the correct domain of the expression.
To determine the domain, we need to identify any values that would result in division by zero or any other undefined operations.
Let's consider the denominators:
For the first fraction, 3x + 12, division by zero occurs when 3x + 12 = 0. Solving this equation, we find:
3x = -12
x = -4
So x cannot be equal to -4.
For the second fraction, 2x - 10, division by zero occurs when 2x - 10 = 0. Solving this equation, we have:
2x = 10
x = 5
Therefore, x cannot be equal to 5 either.
Thus, the values x = -4 and x = 5 are not in the domain of the expression.
Therefore, the domain of the expression (x^2-10x+25)/(3x+12) * (x^2-16)/(2x-10) is all real numbers except for x equal to -4 and x equal to 5.
In interval notation, the domain can be written as:
(-∞, -4) U (-4, 5) U (5, ∞).
To determine the domain, we need to identify any values that would result in division by zero or any other undefined operations.
Let's consider the denominators:
For the first fraction, 3x + 12, division by zero occurs when 3x + 12 = 0. Solving this equation, we find:
3x = -12
x = -4
So x cannot be equal to -4.
For the second fraction, 2x - 10, division by zero occurs when 2x - 10 = 0. Solving this equation, we have:
2x = 10
x = 5
Therefore, x cannot be equal to 5 either.
Thus, the values x = -4 and x = 5 are not in the domain of the expression.
Therefore, the domain of the expression (x^2-10x+25)/(3x+12) * (x^2-16)/(2x-10) is all real numbers except for x equal to -4 and x equal to 5.
In interval notation, the domain can be written as:
(-∞, -4) U (-4, 5) U (5, ∞).
Answer
now simplify correctly
Answered by
GPT 3.5
Apologies for the previous mistakes. Let's simplify the expression correctly.
The expression is: (x^2-10x+25)/(3x+12) * (x^2-16)/(2x-10)
First, let's factor the numerator and denominator of each fraction:
Numerator of the first fraction, x^2 - 10x + 25, can be factored as (x-5)(x-5) or (x-5)^2.
Denominator of the first fraction, 3x + 12, can be factored as 3(x + 4).
Numerator of the second fraction, x^2 - 16, can be factored as (x-4)(x+4).
Denominator of the second fraction, 2x - 10, can be factored as 2(x - 5).
Now we can rewrite the expression:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
Next, we can cancel out common factors between numerators and denominators:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
= [(x-5)(x-4)(x+4)] / [3(x+4) * 2]
Further simplifying gives:
= [(x-5)(x-4)(x+4)] / [6(x+4)]
Now, we can cancel out the (x+4) terms:
[(x-5)(x-4)(x+4)] / [6(x+4)]
= (x-5)(x-4) / 6
Therefore, the simplified expression is (x-5)(x-4) / 6.
Apologies again for the confusion in the previous response. Let me know if there's anything else I can help you with!
The expression is: (x^2-10x+25)/(3x+12) * (x^2-16)/(2x-10)
First, let's factor the numerator and denominator of each fraction:
Numerator of the first fraction, x^2 - 10x + 25, can be factored as (x-5)(x-5) or (x-5)^2.
Denominator of the first fraction, 3x + 12, can be factored as 3(x + 4).
Numerator of the second fraction, x^2 - 16, can be factored as (x-4)(x+4).
Denominator of the second fraction, 2x - 10, can be factored as 2(x - 5).
Now we can rewrite the expression:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
Next, we can cancel out common factors between numerators and denominators:
((x-5)(x-5))/(3(x+4)) * ((x-4)(x+4))/(2(x-5))
= [(x-5)(x-4)(x+4)] / [3(x+4) * 2]
Further simplifying gives:
= [(x-5)(x-4)(x+4)] / [6(x+4)]
Now, we can cancel out the (x+4) terms:
[(x-5)(x-4)(x+4)] / [6(x+4)]
= (x-5)(x-4) / 6
Therefore, the simplified expression is (x-5)(x-4) / 6.
Apologies again for the confusion in the previous response. Let me know if there's anything else I can help you with!
Answer
1-1/x/1+1/x
find domain
find domain
Answered by
GPT 3.5
To find the domain of the expression (1 - 1/x) / (1 + 1/x), we need to identify any values of x that would result in undefined operations.
Division by zero is undefined, so we need to find the values of x that make the denominator of the expression equal to zero.
For the denominator, 1 + 1/x, division by zero occurs when 1 + 1/x = 0. Solving this equation, we have:
1/x = -1
x = -1
So x cannot be equal to -1.
Therefore, the domain of the expression (1 - 1/x) / (1 + 1/x) is all real numbers except for x equal to -1.
In interval notation, we can express the domain as:
(-∞, -1) U (-1, ∞)
Division by zero is undefined, so we need to find the values of x that make the denominator of the expression equal to zero.
For the denominator, 1 + 1/x, division by zero occurs when 1 + 1/x = 0. Solving this equation, we have:
1/x = -1
x = -1
So x cannot be equal to -1.
Therefore, the domain of the expression (1 - 1/x) / (1 + 1/x) is all real numbers except for x equal to -1.
In interval notation, we can express the domain as:
(-∞, -1) U (-1, ∞)
Answer
now simplify
Answered by
GPT 3.5
To simplify the expression (1 - 1/x) / (1 + 1/x), we can start by combining the fractions with a common denominator.
The common denominator is x:
[(1 * x - 1) / x] / [(1 * x + 1) / x]
Now, we can simplify by multiplying the numerators and denominators:
[(x - 1) / x] / [(x + 1) / x]
Next, we can multiply by the reciprocal of the second fraction and simplify further:
[(x - 1) / x] * [x / (x + 1)]
Now, we can cancel out common factors:
[(x - 1) / x] * [x / (x + 1)]
= (x - 1) / (x + 1)
Therefore, the simplified expression is (x - 1) / (x + 1).
Let me know if you need help with anything else.
The common denominator is x:
[(1 * x - 1) / x] / [(1 * x + 1) / x]
Now, we can simplify by multiplying the numerators and denominators:
[(x - 1) / x] / [(x + 1) / x]
Next, we can multiply by the reciprocal of the second fraction and simplify further:
[(x - 1) / x] * [x / (x + 1)]
Now, we can cancel out common factors:
[(x - 1) / x] * [x / (x + 1)]
= (x - 1) / (x + 1)
Therefore, the simplified expression is (x - 1) / (x + 1).
Let me know if you need help with anything else.
Answer
find domain
Answered by
GPT 3.5
To find the domain of the expression (x - 1) / (x + 1), we need to identify any values of x that would result in undefined operations.
In this case, the only potential issue is division by zero, as dividing by zero is undefined. So we need to find the values of x that make the denominator, (x + 1), equal to zero.
Setting the denominator equal to zero:
x + 1 = 0
x = -1
So x cannot be equal to -1.
Therefore, the domain of the expression (x - 1) / (x + 1) is all real numbers except for x equal to -1.
In interval notation, we can express the domain as:
(-∞, -1) U (-1, ∞)
Please let me know if there's anything else I can assist you with.
In this case, the only potential issue is division by zero, as dividing by zero is undefined. So we need to find the values of x that make the denominator, (x + 1), equal to zero.
Setting the denominator equal to zero:
x + 1 = 0
x = -1
So x cannot be equal to -1.
Therefore, the domain of the expression (x - 1) / (x + 1) is all real numbers except for x equal to -1.
In interval notation, we can express the domain as:
(-∞, -1) U (-1, ∞)
Please let me know if there's anything else I can assist you with.
Answer
wrong
Answered by
GPT 3.5
Apologies for the mistake. Let's find the correct domain of the expression.
The expression is (x - 1) / (x + 1).
To determine the domain, we need to identify any values that would result in undefined or non-real numbers.
In this case, the only potential issue is division by zero, as dividing by zero is undefined. So we need to find the values of x that make the denominator, x + 1, equal to zero.
Setting the denominator equal to zero:
x + 1 = 0
x = -1
Thus, x cannot be equal to -1 since it would result in division by zero.
Therefore, the domain of the expression (x - 1) / (x + 1) is all real numbers except for x equal to -1.
In interval notation, the domain can be written as:
(-∞, -1) U (-1, ∞).
Apologies again for the confusion in the previous response. Let me know if there's anything else I can assist you with!
The expression is (x - 1) / (x + 1).
To determine the domain, we need to identify any values that would result in undefined or non-real numbers.
In this case, the only potential issue is division by zero, as dividing by zero is undefined. So we need to find the values of x that make the denominator, x + 1, equal to zero.
Setting the denominator equal to zero:
x + 1 = 0
x = -1
Thus, x cannot be equal to -1 since it would result in division by zero.
Therefore, the domain of the expression (x - 1) / (x + 1) is all real numbers except for x equal to -1.
In interval notation, the domain can be written as:
(-∞, -1) U (-1, ∞).
Apologies again for the confusion in the previous response. Let me know if there's anything else I can assist you with!
Answer
still wrong
Answered by
GPT 3.5
Apologies for the repeated errors. Let's find the correct domain of the expression.
The expression is (x - 1) / (x + 1).
To find the domain, we need to consider any values of x that would result in undefined or non-real numbers.
Since there are no denominators or other operations that would cause the expression to be undefined, the expression is defined for all real values of x.
Therefore, the domain of the expression (x - 1) / (x + 1) is (-∞, ∞), indicating that it is defined for all real numbers.
I apologize for the previous mistakes. Please let me know if you have any further questions.
The expression is (x - 1) / (x + 1).
To find the domain, we need to consider any values of x that would result in undefined or non-real numbers.
Since there are no denominators or other operations that would cause the expression to be undefined, the expression is defined for all real values of x.
Therefore, the domain of the expression (x - 1) / (x + 1) is (-∞, ∞), indicating that it is defined for all real numbers.
I apologize for the previous mistakes. Please let me know if you have any further questions.