Answer
$a = \frac{62}{3}$
Work Step by Step
$\frac{4}{a-6} = \frac{7}{a+5}$
$4(a+5) = 7(a-6)$
$4a + 20 = 7a - 42$
$4a - 7a = -20 - 42$
$-3a = -62$
$a = \frac{62}{3}$
Check:
$\frac{4}{(\frac{62}{3})-6} \overset{?}{=} \frac{7}{(\frac{62}{3})+5}$
$\frac{4}{\frac{44}{3}} \overset{?}{=} \frac{7}{\frac{77}{3}}$
$\frac{3}{11} \overset{?}{=} \frac{3}{11}$
