# Chapter 1, Equations and Graphs - Section 1.6 - Solving Other Types of Equations - 1.6 Exercises - Page 138: 31

$x=\pm\sqrt{2}$

#### Work Step by Step

$1+\displaystyle \frac{1}{(x+1)(x+2)}=\frac{2}{x+1}+\frac{1}{x+2}$ We multiply through by $(x+1)(x+2)$: $(x+1)(x+2)+1=2(x+2)+(x+1)$ And distribute: $x^{2}+3x+2+1=2x+4+x+1$ And simplify: $x^{2}+3x+2+1-2x-4-x-1=0$ $x^{2}-2=0$ $x=\pm\sqrt{2}$

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