Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.5 - Equations - 1.5 Exercises - Page 57: 88

Answer

This equation has no real solutions.

Work Step by Step

$\dfrac{1}{x-1}-\dfrac{2}{x^{2}}=0$ Evaluate the substraction: $\dfrac{x^{2}-2(x-1)}{x^{2}(x-1)}=0$ Take $x^{2}(x-1)$ to multiply the right side. We are left with: $x^{2}-2x+2=0$ Solve using the quadratic formula. Here, $a=1$, $b=-2$ and $c=2$: $x=\dfrac{-(-2)\pm\sqrt{(-2)^{2}-4(1)(2)}}{2(1)}=\dfrac{2\pm\sqrt{4-8}}{2}=\dfrac{2\pm\sqrt{-4}}{2}$ $x=\dfrac{2\pm2i}{2}=1\pm i$
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