Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 11 - Section 11.3 - Solving Equations by Using Quadratic Methods - Exercise Set: 9

Answer

$x=\dfrac{3}{4}\pm\dfrac{\sqrt{57}}{4}$

Work Step by Step

$\dfrac{3}{x}+\dfrac{4}{x+2}=2$ Multiply the whole equation by $x(x+2)$: $x(x+2)\Big(\dfrac{3}{x}+\dfrac{4}{x+2}=2\Big)$ $3(x+2)+4x=2x(x+2)$ $3x+6+4x=2x^{2}+4x$ Take all terms to the right side of the equation and simplify it: $0=2x^{2}+4x-3x-4x-6$ $2x^{2}-3x-6=0$ Use the quadratic formula to solve this equation. The formula is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. Here, $a=2$, $b=-3$ and $c=-6$. Substitute the known values into the formula and simplify: $x=\dfrac{-(-3)\pm\sqrt{(-3)^{2}-4(2)(-6)}}{2(2)}=\dfrac{3\pm\sqrt{9+48}}{4}=...$ $...=\dfrac{3\pm\sqrt{57}}{4}=\dfrac{3}{4}\pm\dfrac{\sqrt{57}}{4}$ The original equation is not undefined for neither of the values of $x$ found. Our final answer is $x=\dfrac{3}{4}\pm\dfrac{\sqrt{57}}{4}$
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