Answer
$ \displaystyle \frac{8x+7}{2x^{2}}$
Work Step by Step
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad x.$
List of factors of the second denominator: $\qquad 2,x,x$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $List$=x...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
(one $x$ is already in, we add the other $x$ and the $2$ to the list)
List = $x,x,2,$
$LCD=2x^{2}$
Step 2. Rewrite each expression with the LCD:
$\displaystyle \frac{4}{x}\cdot\frac{2x}{2x}+\frac{7}{2x^{2}}=\frac{8x}{2x^{2}}+\frac{7}{2x^{2}}=...$
Step 3. Combine numerators over the LCD
$=\displaystyle \frac{8x+7}{2x^{2}}$
Step 4. Simplify, if possible.
... nothing to simplify
=$ \displaystyle \frac{8x+7}{2x^{2}}$
