Algebra: A Combined Approach (4th Edition)

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

Chapter 10 - Cumulative Review - Page 754: 28

Answer

$a= -5, -1$

Work Step by Step

$\frac {28}{9-a^2} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {28}{(3+a)(3-a)} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {28}{(3+a)(-3+a)(-1)} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {-28}{(3+a)(-3+a)} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {-28}{(a+3)(a-3)} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {-28}{(a+3)(a-3)}*(a+3)=\frac{2a}{a-3}*(a+3) + \frac{6}{a+3}*(a+3)$ $\frac {-28}{(a-3)}=\frac{2a(a+3)}{a-3} + 6$ $\frac {-28}{(a-3)}*(a-3)=\frac{2a(a+3)}{a-3}*(a-3) + 6*(a-3)$ $-28=2a(a+3)+6*(a-3)$ $-28=2a^2+6a+6a-18$ $-28=2a^2+12a-18$ $-28+28=2a^2+12a-18+28$ $0=2a^2+12a+10$ $0=2(a^2+6a+5)$ $0=2(a+5)(a+1)$ $0\ne2$ $0=a+5$ $0-5=a+5-5$ $-5=a$ $0=a+1$ $0-1=a+1-1$ $-1=a$ $a=-5$ $\frac {28}{9-a^2} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {28}{9-(-5)^2} =\frac{2*(-5)}{(-5)-3} + \frac{6}{(-5)+3}$ $\frac {28}{9-25} =\frac{-10}{-8} + \frac{6}{-2}$ $\frac {28}{-16} =\frac{5}{4} + (-3)$ $\frac {7}{-4} = 5/4 -3$ $-7/4 = 5/4 -3$ $-7/4 =5/4 -12/4$ $-7/4 = -7/4$ (true) $a=-1$ $\frac {28}{9-a^2} =\frac{2a}{a-3} + \frac{6}{a+3}$ $\frac {28}{9-(-1)^2} =\frac{2*(-1)}{(-1)-3} + \frac{6}{(-1)+3}$ $\frac {28}{9-1} =\frac{-2}{-4} + \frac{6}{2}$ $\frac {28}{8} = 1/2 + 3$ $14/4 = 7/2$ $7/2 = 7/2$ (true)
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