Question

In the following exercise solve$\frac{3}{q+8}-\frac{2}{q-2}=1$

Short answer

The solution is$q=-2andq=-3$

Step-by-step solution

Step 1. Given information

$\frac{3}{q+8}-\frac{2}{q-2}=1$

Step 2. Solve.

The least common denominator of all denominators in the equation is $\left(q+8\right)\left(q-2\right)$

Clear the fraction by multiplying both sides of the equation by the LCD.

$$\begin{gathered} \left(q+8\right)\left(q-2\right)\left(\frac{3}{q+8}-\frac{2}{q-2}\right)=\left(q+8\right)\left(q-2\right)\left(1\right) \\ \left(q+8\right)\left(q-2\right)\left(\frac{3}{q+8}\right)-\left(q+8\right)\left(q-2\right)\left(\frac{2}{q-2}\right)=\left(q+8\right)\left(q-2\right)\left(1\right) \\ 3\left(q-2\right)-2\left(q+8\right)=\left(q+8\right)\left(q-2\right) \\ q-22=\left(q+8\right)\left(q-2\right) \\ {q}^2+5q+6=0 \\ \left(q+3\right)\left(q+2\right) \\ q=-3orq=-2 \end{gathered}$$