Rewriting the first term, we have:
[tex]\begin{gathered} \frac{7}{x^2-7x+10} \\ \frac{7}{(x-5)(x-2)}(\text{ Factoring the quadratic expression}) \\ \frac{7\cdot(x-6)}{(x-5)(x-2)(x-6)}(\text{ Multiplying on both sides by (x-6))} \\ \frac{7x-42}{(x-5)(x-2)(x-6)}(\text{ Distributing)} \end{gathered}[/tex]Rewriting the second term, we have:
[tex]\begin{gathered} \frac{4x}{x^2-8x+12} \\ \frac{4x}{(x-6)(x-2)}(\text{ Factoring the quadratic expression}) \\ \frac{4x\cdot(x-5)}{(x-6)(x-2)(x-5)}(\text{ Multiplying on both sides by (x-5))} \\ \frac{4x^2-20x}{(x-6)(x-2)(x-5)}(\text{ Distributing)} \end{gathered}[/tex]The answers are:
[tex]\frac{7x-42}{(x-5)(x-2)(x-6)},\frac{4x^2-20x}{(x-6)(x-2)(x-5)}[/tex]