Answer
$ -\displaystyle \frac{7}{x+7}$
Work Step by Step
$\displaystyle \frac{x}{x+7}-1=\frac{x}{x+7}-\frac{1}{1}$
Step 1: Find the LCD.
List of factors of the first denominator: $\qquad (x+7)$
List of factors of the second denominator: $\qquad 1$
Build the LCD:
- write all factors of the 1st denominator:$\qquad $
List$= (x+7),...\quad$ (for now)
- add to the list factors of the second denominator that are not already on the list
($1$ is added to the list)
List = $(x+7),1$
$LCD=(x+7)$
Step 2. Rewrite each expression with the LCD:
$=\displaystyle \frac{x}{x+7}-\frac{1}{1}\cdot\frac{(x+7)}{(x+7)}= \frac{x}{x+7} -\frac{x+7}{x+7}=...$
Step 3. Combine numerators over the LCD
$=$ $ \displaystyle \frac{x-(x+7)}{x+7} $
Step 4. Simplify, if possible.
$= \displaystyle \frac{x-x-7}{x+7}$
= $ -\displaystyle \frac{7}{x+7}$
