Question
Fully simplify the expression below and write your answer as a single fraction.
start fraction, 2, x, squared, minus, 32, divided by, x, cubed, plus, 9, x, squared, plus, 20, x, end fraction, dot, start fraction, x, cubed, plus, 5, x, squared, divided by, x, squared, minus, 9, x, plus, 20, end fraction
start fraction, 2, x, squared, minus, 32, divided by, x, cubed, plus, 9, x, squared, plus, 20, x, end fraction, dot, start fraction, x, cubed, plus, 5, x, squared, divided by, x, squared, minus, 9, x, plus, 20, end fraction
Answers
Answer
wrong
Answer
it's not the correct answer
Answered by
GPT 3.5
The expression simplifies to:
(x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20)
The common factors in the numerators and denominators cancel out, resulting in:
(x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20) = (x^2 - 32) / (x^2 - 9x + 20)
Therefore, the expression fully simplifies to:
(x^2 - 32) / (x^2 - 9x + 20)
(x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20)
The common factors in the numerators and denominators cancel out, resulting in:
(x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20) = (x^2 - 32) / (x^2 - 9x + 20)
Therefore, the expression fully simplifies to:
(x^2 - 32) / (x^2 - 9x + 20)
Answered by
GPT 3.5
I apologize for the error. Let's simplify the expression again:
Starting expression: (2x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20)
Factors can be simplified as follows:
2x^2 - 32 = 2(x^2 - 16) = 2(x + 4)(x - 4)
x^3 + 9x^2 + 20x = x(x^2 + 9x + 20) = x(x + 4)(x + 5)
(x^3 + 5x^2) = x^2(x + 5)
x^2 - 9x + 20 = (x - 4)(x - 5)
The expression now simplifies to:
[ 2(x + 4)(x - 4) / x(x + 4)(x + 5) ] * [ x^2(x + 5) / (x - 4)(x - 5) ]
The (x + 4) and (x - 4) terms in the numerators and denominators cancel out, and we are left with:
2 / x(x + 5)(x - 5)
Therefore, the expression fully simplifies to:
2 / x(x + 5)(x - 5)
Starting expression: (2x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20)
Factors can be simplified as follows:
2x^2 - 32 = 2(x^2 - 16) = 2(x + 4)(x - 4)
x^3 + 9x^2 + 20x = x(x^2 + 9x + 20) = x(x + 4)(x + 5)
(x^3 + 5x^2) = x^2(x + 5)
x^2 - 9x + 20 = (x - 4)(x - 5)
The expression now simplifies to:
[ 2(x + 4)(x - 4) / x(x + 4)(x + 5) ] * [ x^2(x + 5) / (x - 4)(x - 5) ]
The (x + 4) and (x - 4) terms in the numerators and denominators cancel out, and we are left with:
2 / x(x + 5)(x - 5)
Therefore, the expression fully simplifies to:
2 / x(x + 5)(x - 5)
Answered by
GPT 3.5
I apologize for the mistake. Let's try simplifying the expression again:
Given expression:
(2x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20)
Factor the numerators and denominators:
2(x^2 - 16) / x(x + 4)(x + 5) * x^2(x + 5) / (x - 4)(x - 5)
The (x^2 - 16) can be further factored to (x + 4)(x - 4):
2(x + 4)(x - 4) / x(x + 4)(x + 5) * x^2(x + 5) / (x - 4)(x - 5)
Now we can cancel out common factors:
2(x - 4) / x(x + 5) * x^2 / (x - 5)
Multiplying the remaining terms:
2x(x - 4) / x(x + 5) * x^2 / (x - 5)
Cancel out common factors:
2(x - 4) / (x + 5) * x / (x - 5)
Now multiply:
2x(x - 4) / (x + 5)(x - 5)
Simplify this expression gives the final answer:
2x^2 - 8x / (x^2 - 5x + 5x - 25)
2x(x - 4) / (x(x - 5) + 5(x - 5))
2x(x - 4) / ((x + 5)(x - 5))
2x(x - 4) / (x^2 - 25)
Therefore, the fully simplified expression is:
2x(x - 4) / (x^2 - 25)
Given expression:
(2x^2 - 32) / (x^3 + 9x^2 + 20x) * (x^3 + 5x^2) / (x^2 - 9x + 20)
Factor the numerators and denominators:
2(x^2 - 16) / x(x + 4)(x + 5) * x^2(x + 5) / (x - 4)(x - 5)
The (x^2 - 16) can be further factored to (x + 4)(x - 4):
2(x + 4)(x - 4) / x(x + 4)(x + 5) * x^2(x + 5) / (x - 4)(x - 5)
Now we can cancel out common factors:
2(x - 4) / x(x + 5) * x^2 / (x - 5)
Multiplying the remaining terms:
2x(x - 4) / x(x + 5) * x^2 / (x - 5)
Cancel out common factors:
2(x - 4) / (x + 5) * x / (x - 5)
Now multiply:
2x(x - 4) / (x + 5)(x - 5)
Simplify this expression gives the final answer:
2x^2 - 8x / (x^2 - 5x + 5x - 25)
2x(x - 4) / (x(x - 5) + 5(x - 5))
2x(x - 4) / ((x + 5)(x - 5))
2x(x - 4) / (x^2 - 25)
Therefore, the fully simplified expression is:
2x(x - 4) / (x^2 - 25)