Question

In the following exercises, add.

$\frac{2r^2}{2r-1}+\frac{15r-8}{2r-1}$

Short answer

The simplified expression is$r+8$but$r\ne \frac{1}{2}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{2r^2}{2r-1}+\frac{15r-8}{2r-1}$

Step 2. Add the numerator

As the denominator is the same for both the terms, add the numerator and place it over the common denominator.

$\frac{2r^2}{2r-1}+\frac{15r-8}{2r-1}=\frac{2r^2+15r-8}{2r-1}$

Step 3. Factor the numerator

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

$\frac{(2r-1)(r+8)}{(2r-1)}=r+8$

• So, the resultant expression is $r+8$but the denominator of the given expression was $2r-1$, so, $r\ne \frac{1}{2}$.