Question

In the following exercises, add or subtract.

$\frac{20w}{5w-2}+\frac{5w+6}{2-5w}$

Short answer

The sum of the given expressions is 3.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{20w}{5w-2}+\frac{5w+6}{2-5w}$.

Step 2. Multiply the second term by -1-1

Multiply the numerator and denominator of the second term by $-1$.

$\frac{20w}{5w-2}+\frac{5w+6}{2-5w}=\frac{20w}{5w-2}+\frac{-5w-6}{5w-2}$

Step 3. Add the numerators

• As the denominator is same for both the terms, add the numerator and place over the common denominator.
• Add the like terms of the numerator.

$\begin{array}{rcl}\frac{20w}{5w-2}+\frac{-5w-6}{5w-2}& =& \frac{20w-5w-6}{5w-2}\\ & =& \frac{15w-6}{5w-2}\end{array}$

Step 4. Simplify 

• Factor the expression in the numerator and then cancel out the common terms in numerator and denominator.

$\begin{array}{rcl}\frac{15w-6}{5w-2}& =& \frac{3\cancel{\left(5w-2\right)}}{\cancel{5w-2}}\\ & =& 3\end{array}$