Question

In the following exercises, perform indicated operations.

$\frac{2x+7}{10x-1}+3$

Short answer

The resultant expression is$\frac{4\left(x+8\right)}{10x-1}$.

Step-by-step solution

Step 1. GIven Information

The given expression is$\frac{2x+7}{10x-1}+3$.

Step 2. Express with LCD

Step 2. Express with LCD

• The LCD of the given terms is $10x-1$.
• Express the given expression with the LCD.

$\frac{2x+7}{10x-1}+3=\frac{2x+7}{10x-1}+\frac{30x-3}{10x-1}$

Step 3. Simplify

• As the denominator is the same for both the terms, perform addition in the numerator and place it over the common denominator.

$\begin{array}{rcl}\frac{2x+7+30x-3}{10x-1}& =& \frac{32x+4}{10x-1}\\ & =& \frac{4\left(x+8\right)}{10x-1}\end{array}$

• So, the resultant expression is$\frac{4\left(x+8\right)}{10x-1}$.