Question

Multiply and Simplify your Answer. Type Answer in Factored Form.

Answer 1

Step 1:

Write the expression

`(x^2+10x+25)/(4x^2-100)\text{ . }\frac{5x\text{ - 25}}{2x}`

Step 2:

Factorize all expressions and cancel out common factors.

`\begin{gathered} \frac{(\text{x + 5)(x + 5)}}{(2x)^2-10^2}\text{ . }\frac{5(x\text{ - 5)}}{2x} \\ ((x+5)^2)/((2x-10)(2x+10))\text{ . }\frac{5(\text{x - 5)}}{2x} \\ \frac{5(x+5)^2(x\text{ - 5)}}{2x(2x\text{ - 10)(2x + 10)}} \\ =\text{ }\frac{5(x+5)^2(\text{x - 5)}}{2*2*2x(\text{x + 5)(x - 5)}} \\ =\text{ }\frac{5(x+5)^2(\text{ x- 5)}}{8x(x\text{ + 5)(x - 5)}} \\ \text{= }\frac{5(\text{x + 5)}}{8x} \end{gathered}`

Final answer

`\frac{5(x\text{ + 5)}}{8x}`