# Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set - Page 523: 8

The solutions are -1 and 7

#### Work Step by Step

6+$\frac{5}{y}$=y-$\frac{2}{y}$ y(6+$\frac{5}{y}$)=y(y-$\frac{2}{y}$) 6y+y$\frac{5}{y}$=y*y-y$\frac{2}{y}$ 6y+5=$y^{2}$-2 0=$y^{2}$-2-6y-5 0=$y^{2}$-6y-7 0=$y^{2}$+y-7y-7 0=y(y+1)-7(y+1) 0=(y-7)(y+1) y-7=0 or y+1=0 y=7 or y=-1 The solutions are -1 and 7 Check Let y=-1 6+$\frac{5}{y}$=y-$\frac{2}{y}$ 6+$\frac{5}{-1}$=-1-$\frac{2}{-1}$ 6-5=-1+2 1=1 Let y=7 6+$\frac{5}{y}$=y-$\frac{2}{y}$ 6+$\frac{5}{7}$=7-$\frac{2}{7}$ $\frac{42}{7}$+$\frac{5}{7}$=$\frac{49}{7}$-$\frac{2}{7}$ $\frac{47}{7}$=$\frac{47}{47}$

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