Chapter 8.2, Problem 64HP

To determine

To state: the equation is true or false.

Answer to Problem 64HP

The equation is true.

Explanation of Solution

Given information:

The equation is $\frac{6}{x+2}+\frac{4}{x-3}=\frac{10x-10}{\left(x+2\right)\left(x-3\right)}$ .

to state true of false, first simplify and then LCM of denominator and then simplify,

  $\begin{array}{l}\frac{6}{x+2}+\frac{4}{x-3}=\frac{10x-10}{\left(x+2\right)\left(x-3\right)}\\ \frac{6\left(x-3\right)+4\left(x+2\right)}{\left(x+2\right)\left(x-3\right)}=\frac{10x-10}{\left(x+2\right)\left(x-3\right)}\text{ [LCM of denominator and simplify]}\\ \frac{6x-18+4x+8}{\left(x+2\right)\left(x+3\right)}=\frac{10x-10}{\left(x+2\right)\left(x-3\right)}\text{ [multiply]}\\ \frac{10x-10}{\left(x+2\right)\left(x-3\right)}=\frac{10x-10}{\left(x+2\right)\left(x-3\right)}\end{array}$