Chapter 11 - Rational Expressions and Functions - 11-5 Solving Rational Equations - Practice and Problem-Solving Exercises - Page 683: 25

$x=3$

Given: $5(x+1)=(x+1)(x+2)$ $5x+5=x^2+2x+x+2$ $5x+5=x^2+3x+2$ $x^2+3x+2-5x-2=0$ $x^2-2x-3=0$ $x^2+x-3x-3$ $x(x+1)-3(x+1)$ $(x-3)(x+1)=0$ Solutions are: $x=3,-1$ For $x=-1$ the equation becomes undefined so the suitable answer is $x=3$