Fully simplify the expression below and write your answer as a single fraction.

Question

2x^2 -32 over x^3 +9x^2 +20x multiply by x^3 + 5x^2 over x^2 -9x +20

Answer 1

First, factor all the denominators:

x^3 + 9x^2 + 20x = x(x^2 + 9x + 20) = x(x + 5)(x + 4)

x^2 - 9x + 20 = (x - 4)(x - 5)

Now, the expression becomes:

(2x^2 - 32) / (x(x + 5)(x + 4)) * (x^3 + 5x^2) / (x - 4)(x - 5)

Simplify the expression by canceling common factors:

= 2(x - 4)(x + 4) / (x)(x + 5) * x^2(x + 5) / (x - 4)(x - 5)
= 2(x - 4)x^2 / (x + 5)(x)(x - 5)
= 2x^3 - 8x^2 / x(x + 5)(x - 5)
= 2x^2(x - 4) / x(x + 5)(x - 5)
= 2x(x - 4) / (x + 5)(x - 5)
= 2(x^2 - 4x) / (x + 5)(x - 5)
= 2x(x - 4) / (x + 5)(x - 5)

Therefore, the simplified expression is 2x(x - 4) / (x + 5)(x - 5).

Answer 2

try simplify further

Answer 3

Apologies for the oversight. Let's simplify further:

2x(x - 4) / (x + 5)(x - 5)

Expanding the numerator:

2x^2 - 8x

Final simplified expression:

(2x^2 - 8x) / [(x + 5)(x - 5)]

Factoring out 2x from the numerator:

2x(x - 4) / [(x + 5)(x - 5)]

Therefore, the single fraction expression after fully simplifying is:

2x(x - 4) / (x + 5)(x - 5)

Answer 4

resolve the equation again

Answer 5

The simplified expression we have is:

2x(x - 4) / (x + 5)(x - 5)

To resolve this equation, we will set the numerator equal to zero and solve for x:

2x(x - 4) = 0

Setting each factor to zero:

2x = 0 or (x - 4) = 0

From the first equation, we get:

x = 0

From the second equation:

x = 4

Therefore, the solution to the equation is x = 0 or x = 4.