## Elementary Algebra

Published by Cengage Learning

# Chapter 10 - Quadratic Equations - Chapter 10 Test - Page 469: 13

#### 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: $\frac{x-2}{3} = \frac{4}{x+1}$ $(x-2)(x+1) = 4(3)$ $x(x+1)-2(x+1) = 12$ $x^{2} + x - 2x - 2 - 12 = 0$ $x^{2} -x - 14 = 0$ $x = \frac{-b±\sqrt {b^{2}-4ac}}{2a}$ $x = \frac{-(-1)±\sqrt {(-1)^{2}-4(1)(-14)}}{2(1)}$ $x = \frac{1±\sqrt {1+56}}{2}$ $x = \frac{1±\sqrt {57}}{2}$

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