Step 1:
Write the expression
[tex]\frac{x^2+10x+25}{4x^2-100}\text{ . }\frac{5x\text{ - 25}}{2x}[/tex]
Step 2:
Factorize all expressions and cancel out common factors.
[tex]\begin{gathered} \frac{(\text{x + 5)(x + 5)}}{(2x)^2-10^2}\text{ . }\frac{5(x\text{ - 5)}}{2x} \\ \frac{(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\times2\times2x(\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}[/tex]
Final answer
[tex]\frac{5(x\text{ + 5)}}{8x}[/tex]
