Answer
{$-\frac{8}{5},1$}
Work Step by Step
We will first cross multiply the fractions together in order to create a quadratic equation:
$\frac{5x-2}{3}=\frac{2}{x+1}$
$(5x-2)(x+1)=2(3)$
$5x(x+1)-2(x+1)=6$
$5x^{2}+5x-2x-2=6$
$5x^{2}+3x-2-6=0$
$5x^{2}+3x-8=0$
Now, we will factor this quadratic equation using the rules of factoring trinomials:
$5x^{2}+3x-8=0$
$5x^{2}-5x+8x-8=0$
$5x(x-1)+8(x-1)=0$
$(x-1)(5x+8)=0$
$(x-1)=0$ or $(5x+8)=0$
$x=1$ or $x=-\frac{8}{5}$
Therefore, the solution set is {$-\frac{8}{5},1$}.
