Answer
$x=\frac{23}{6}$
Work Step by Step
$\frac{1}{x-2}=\frac{10}{4x+3}$
$1(4x+3)=10(x-2)$
$4x+3=10x-20$
$4x-10x=-20-3$
$-6x=-23$
$x=\frac{-23}{-6}=\frac{23}{6}$
Check the solution:
$\frac{1}{\frac{23}{6}-2}=\frac{10}{4(\frac{23}{6})+3}$
$\frac{1}{\frac{11}{6}}=\frac{10}{\frac{46}{3}+3}$
$1·\frac{6}{11}=\frac{10}{\frac{55}{3}}$
$\frac{6}{11}=10·\frac{3}{55}$
$\frac{6}{11}=\frac{6}{11}$
