# Chapter 7 - Section 7.5 - Solving Equations Containing Rational Expressions - Exercise Set: 36

the solutions are -1 and 16

#### Work Step by Step

$\frac{15}{x+4}$=$\frac{x-4}{x}$ x(x+4)$\frac{15}{x+4}$=x(x+4)$\frac{x-4}{x}$ $\frac{15}{x+4}$=$\frac{x-4}{x}$ 15x=$x^{2}$-16 0=$x^{2}$-15x-16 0=$x^{2}$+x-16x-16 0=x(x+1)-16(x+1) 0=(x-16)(x+1) x-16=0 or x+1=0 x=16 or x=-1 the solutions are -1 and 16 Check Let x=-1 $\frac{15}{-1+4}$=$\frac{-1-4}{-1}$ $\frac{15}{-3}$=$\frac{-5}{-1}$ -5=-5 Let x=16 $\frac{15}{16+4}$=$\frac{16-4}{16}$ $\frac{15}{20}$=$\frac{12}{16}$ $\frac{3}{4}$=$\frac{3}{4}$

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