Answer:
[tex]D. \: \frac{10 {x}^{2} + 50x}{ {x}^{2} - 49 } [/tex]
Step-by-step explanation:
The given rational expression is
[tex] \frac{x + 5}{x + 7} \cdot \frac{10x}{x - 7} [/tex]
We multiply to obtain:
[tex] \frac{10x(x + 5)}{(x + 7)(x - 7)} [/tex]
Expand the numerator using the distributive property and the denominator using difference of two squares to get:
[tex] \frac{10 {x}^{2} + 50x }{ {x}^{2} - {7}^{2} } [/tex]
This simplifies to
[tex] \frac{10 {x}^{2} + 50x}{ {x}^{2} - 49 } [/tex]
