Answer
$x = \frac{1±\sqrt {57}}{2}$
Work Step by Step
We first cross multiply, and then get all of the terms on one side of the equation. The resulting equation is not easily factorable, so we use the quadratic formula, where the equation is in the form $0=ax^{2}+bx+c$. Thus, we obtain:
$\frac{x-2}{3} = \frac{4}{x+1}$
$(x-2)(x+1) = 4(3)$
$x(x+1)-2(x+1) = 12$
$x^{2} + x - 2x - 2 - 12 = 0$
$x^{2} -x - 14 = 0$
$x = \frac{-b±\sqrt {b^{2}-4ac}}{2a}$
$x = \frac{-(-1)±\sqrt {(-1)^{2}-4(1)(-14)}}{2(1)}$
$x = \frac{1±\sqrt {1+56}}{2}$
$x = \frac{1±\sqrt {57}}{2}$
