Question

In the following exercises, solve.

$\frac{x-10}{x^2+8x+12}=\frac{3}{x+2}+\frac{4}{x+6}$

Short answer

The solution is$x=-6.$

Step-by-step solution

Step 1. Given Information

The given rational expression is

$\frac{x-10}{x^2+8x+12}=\frac{3}{x+2}+\frac{4}{x+6}$

Step 2. Removing the fraction

The Least common denominator is

$(x+2)(x+6)$

Multiply the equation by the LCD,

$$\begin{gathered} (x+2)(x+6)\times \frac{x-10}{x^2+8x+12}=\left[\frac{3}{x+2}+\frac{4}{x+6}\right](x+2)(x+6) \\ {x}^2+8x+12\times \frac{x-10}{x^2+8x+12}=3(x+6)+4(x+2) \\ x-10=3x+18+4x+8 \\ x-10=7x+26 \\ -6x=36 \\ x=-6 \end{gathered}$$