Question

Solve 5 over x plus 8 equals 3 over x for x and determine if the solution is extraneous or not.

Answer 1

$\frac{5}{x+8}=\frac{3}{x}\ \ \ Domain\ D:x+8\neq0\to x\neq-8\ and\ x\neq0\\\\cross\ multiply\\\\5(x)=3(x+8)\ \ \ |use\ distributive\ property\ a(b+c)=ab+ac\\\\5x=3(x)+3(8)\\\\5x=3x+24\ \ \ \ |subtract\ 3x\ from\ both\ sides\\\\2x=24\ \ \ \ |divide\ both\ sides\ by\ 2\\\\\huge\boxed{x=12\in D}$