Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - Chapter 10 Test: 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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