To simplify the expression, we can use long division or polynomial division.
First, let's divide the polynomial 3x^2 - 4x + 13 by x + 3 using long division:
3x - 15
___________________________
x + 3 | 3x^2 - 4x + 13
-(3x^2 + 9x)
-----------------
-13x + 13
-( -13x - 39)
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52
Therefore, 3x^2 - 4x + 13 divided by (x+3) simplifies to 3x - 15 + 52/(x+3).
Simplify
3x2-4x+13 divided by (x+3)
11 answers
Simplify the expression. State any excluded values.
n2+4n-5/n+5
n2+4n-5/n+5
To simplify the expression (n^2 + 4n - 5) / (n + 5), we can either factorize the numerator or use polynomial division. In this case, we will factorize the numerator:
n^2 + 4n - 5 factors to (n + 5)(n - 1).
Therefore, the expression simplifies to (n + 5)(n - 1) / (n + 5). Now, we can cancel out the common factor "n + 5" in the numerator and the denominator:
= (n - 1)
So, the simplified expression is n - 1. The excluded value is n = -5, since it would make the denominator 0.
n^2 + 4n - 5 factors to (n + 5)(n - 1).
Therefore, the expression simplifies to (n + 5)(n - 1) / (n + 5). Now, we can cancel out the common factor "n + 5" in the numerator and the denominator:
= (n - 1)
So, the simplified expression is n - 1. The excluded value is n = -5, since it would make the denominator 0.
Multiply.
3x/2 * x^2-4/12
3x/2 * x^2-4/12
To multiply the expressions (3x/2) and (x^2-4/12), we first simplify each expression separately and then multiply them together.
1. Simplify (x^2-4/12):
x^2 - 4 can be written as (x + 2)(x - 2).
So the expression becomes: (x + 2)(x - 2) / 12
2. Now, multiply the two simplified expressions:
(3x/2) * [(x + 2)(x - 2) / 12]
= (3x/2) * (x + 2)(x - 2) / 12
= (3x/2) * (x^2 - 4) / 12
= (3x/2 * x^2 - 3x/2 * 4) / 12
= (3x^3/2 - 6x/2) / 12
= (3x^3 - 6x) / 24
= (x^3 - 2x) / 8
Therefore, the multiplication of the two expressions becomes (x^3 - 2x) / 8.
1. Simplify (x^2-4/12):
x^2 - 4 can be written as (x + 2)(x - 2).
So the expression becomes: (x + 2)(x - 2) / 12
2. Now, multiply the two simplified expressions:
(3x/2) * [(x + 2)(x - 2) / 12]
= (3x/2) * (x + 2)(x - 2) / 12
= (3x/2) * (x^2 - 4) / 12
= (3x/2 * x^2 - 3x/2 * 4) / 12
= (3x^3/2 - 6x/2) / 12
= (3x^3 - 6x) / 24
= (x^3 - 2x) / 8
Therefore, the multiplication of the two expressions becomes (x^3 - 2x) / 8.
Divide
5xx2+2x / 30x2x+2
5xx2+2x / 30x2x+2
To divide the given expression (5x^2 + 2x) / (30x^2 + 2), we can simplify the expression and perform the division.
Given:
Numerator = 5x^2 + 2x
Denominator = 30x^2 + 2
1. Divide the denominator by 2 to simplify it:
30x^2 + 2 = 2(15x^2 + 1)
The expression becomes: (5x^2 + 2x) / 2(15x^2 + 1)
2. Divide the numerator by 2:
(5x^2 + 2x) / 2 = 5x^2/2 + 2x/2 = (5/2)x^2 + x
Now, we have: [(5/2)x^2 + x] / 2(15x^2 + 1)
3. The division gives us:
[(5/2)x^2 + x] / 2(15x^2 + 1)
= [(5/2)x^2 / (2(15x^2 + 1))] + [x / (2(15x^2 + 1))]
= [5x^2 / 4(15x^2 + 1)] + [x / 2(15x^2 + 1)]
= [5/4] - [x/30x^2 + 2]
Therefore, the simplified expression after division is (5/4) - (x/30x^2 + 2).
Given:
Numerator = 5x^2 + 2x
Denominator = 30x^2 + 2
1. Divide the denominator by 2 to simplify it:
30x^2 + 2 = 2(15x^2 + 1)
The expression becomes: (5x^2 + 2x) / 2(15x^2 + 1)
2. Divide the numerator by 2:
(5x^2 + 2x) / 2 = 5x^2/2 + 2x/2 = (5/2)x^2 + x
Now, we have: [(5/2)x^2 + x] / 2(15x^2 + 1)
3. The division gives us:
[(5/2)x^2 + x] / 2(15x^2 + 1)
= [(5/2)x^2 / (2(15x^2 + 1))] + [x / (2(15x^2 + 1))]
= [5x^2 / 4(15x^2 + 1)] + [x / 2(15x^2 + 1)]
= [5/4] - [x/30x^2 + 2]
Therefore, the simplified expression after division is (5/4) - (x/30x^2 + 2).
5x/x^2+2x divided by 30x^2/x+2
To divide the given expression (5x / x^2 + 2x) by (30x^2 / x + 2), we can simplify the expression and perform the division.
Given:
Numerator = 5x
Denominator = x^2 + 2x
Dividing the first expression by the second expression:
(5x) / (x^2 + 2x)
Factor out x from the denominator:
x(x + 2)
Now the expression becomes:
5x / x(x + 2)
Simplify the expression:
5 / (x + 2)
Given the second part: 30x^2 / (x+2)
Now, divide the expressions:
(5 / (x + 2)) / (30x^2 / (x + 2))
When dividing by a fraction, we can multiply by its reciprocal:
(5 / (x + 2)) * ((x + 2) / 30x^2)
Now simplify:
5 / 30x^2
Which reduces to:
1 / 6x^2
Therefore, the original expression simplifies to (1 / 6x^2).
Given:
Numerator = 5x
Denominator = x^2 + 2x
Dividing the first expression by the second expression:
(5x) / (x^2 + 2x)
Factor out x from the denominator:
x(x + 2)
Now the expression becomes:
5x / x(x + 2)
Simplify the expression:
5 / (x + 2)
Given the second part: 30x^2 / (x+2)
Now, divide the expressions:
(5 / (x + 2)) / (30x^2 / (x + 2))
When dividing by a fraction, we can multiply by its reciprocal:
(5 / (x + 2)) * ((x + 2) / 30x^2)
Now simplify:
5 / 30x^2
Which reduces to:
1 / 6x^2
Therefore, the original expression simplifies to (1 / 6x^2).
Add.
4b-2/3b + b/b+2
4b-2/3b + b/b+2
To add the expressions (4b - 2)/3b + b/(b+2), we first need to find a common denominator in order to combine them.
Given:
(4b - 2)/3b + b/(b+2)
First, the LCD (Least Common Denominator) for these two fractions is 3b(b + 2).
Rewrite each fraction with the LCD as the denominator:
= (4b - 2)(b + 2) / 3b(b + 2) + b * 3b / 3b(b + 2)
Now, we can combine the two fractions since they share the same denominator:
= (4b(b + 2) - 2) / 3b(b + 2) + 3b^2 / 3b(b + 2)
Expand and simplify:
= (4b^2 + 8b - 2) / 3b(b + 2) + 3b^2 / 3b(b + 2)
= (4b^2 + 8b - 2 + 3b^2) / 3b(b + 2)
= (7b^2 + 8b - 2) / 3b(b + 2)
Therefore, the sum of the expressions (4b - 2)/3b + b/(b+2) is (7b^2 + 8b - 2) / 3b(b + 2).
Given:
(4b - 2)/3b + b/(b+2)
First, the LCD (Least Common Denominator) for these two fractions is 3b(b + 2).
Rewrite each fraction with the LCD as the denominator:
= (4b - 2)(b + 2) / 3b(b + 2) + b * 3b / 3b(b + 2)
Now, we can combine the two fractions since they share the same denominator:
= (4b(b + 2) - 2) / 3b(b + 2) + 3b^2 / 3b(b + 2)
Expand and simplify:
= (4b^2 + 8b - 2) / 3b(b + 2) + 3b^2 / 3b(b + 2)
= (4b^2 + 8b - 2 + 3b^2) / 3b(b + 2)
= (7b^2 + 8b - 2) / 3b(b + 2)
Therefore, the sum of the expressions (4b - 2)/3b + b/(b+2) is (7b^2 + 8b - 2) / 3b(b + 2).