Q21. - Algebra 1

Question

Find each sum or difference.
$\frac{1}{x-6}+\frac{3}{x-2}$

Step-by-Step Solution

Answer

$\frac{\mathbf{4}\mathbf{x}\mathbf{-}\mathbf{20}}{\left(x-6\right)\left(x-2\right)}$

Step 1. Multiply.

Multiply numerator and denominator of $\frac{1}{x-6}$ by $\left(x-2\right)$.

$\frac{1}{x-6}\cdot \frac{\left(x-2\right)}{\left(x-2\right)}=\frac{x-2}{\left(x-6\right)\left(x-2\right)}$

Step 2. Multiply.

Multiply numerator and denominator of $\frac{1}{x-2}$ by $\left(x-6\right)$.

$\frac{3}{x-2}\cdot \frac{\left(x-6\right)}{\left(x-6\right)}=\frac{3\left(x-6\right)}{\left(x-2\right)\left(x-6\right)}$

Step 3. Add.

Add two expressions obtained above.

 $\frac{x-2}{\left(x-6\right)\left(x-2\right)}+\frac{3\left(x-6\right)}{\left(x-6\right)\left(x-2\right)}=\frac{x-2+3\left(x-6\right)}{\left(x-6\right)\left(x-2\right)}$

                                                  $$\begin{gathered} =\frac{x-2+3x-18}{\left(x-6\right)\left(x-2\right)} \\ =\frac{4x-20}{\left(x-6\right)\left(x-2\right)} \end{gathered}$$ 

Therefore, the sum of given expression is $\frac{4x-20}{\left(x-6\right)\left(x-2\right)}$.