Answer
$m = \frac{31}{3}$
Work Step by Step
$\frac{2}{m-3} = \frac{5}{m+8}$
$2(m+8) = 5(m-3)$
$2m+16 = 5m - 15$
$2m - 5m = -15 - 16$
$-3m = -31$
$m = \frac{31}{3}$
Check:
$\frac{2}{(\frac{31}{3})-3} \overset{?}{=}\frac{5}{(\frac{31}{3})+8}$
$\frac{2}{7.3333...} \overset{?}{=}\frac{5}{18.3333...}$
$\frac{2}{7.3333...} \overset{?}{=}\frac{5}{18.3333...}$
$0.2727... = 0.2727...$
