Question

In the following exercises, add.

$\frac{3s^2}{3s-2}+\frac{13s-10}{3s-2}$

Short answer

The simplified expression is $s+5$but$s\ne \frac{2}{3}$.

Step-by-step solution

Step 1. Given Information

The given expression is$\frac{3s^2}{3s-2}+\frac{13s-10}{3s-2}$.

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.

$\frac{3s^2}{3s-2}+\frac{13s-10}{3s-2}=\frac{3s^2+13s-10}{3s-2}$

Step 3. Factor the numerator 

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

$\frac{(3s-2)(s+5)}{(3s-2)}=s+5$

• So, the resultant expression is $s+5$but the denominator of the given expression was $3s-2$, so, $s\ne \frac{2}{3}$.