# How do you subtract \frac { 9a - 11x } { 8a } - \frac { 2a - 7x } { 8a }?

May 1, 2018

$\frac{7 a - 4 x}{8 a}$

#### Explanation:

To subtract two rational terms, it is necessary that they have a common denominator. In this case, both terms have a denominator of $8 a$, so the step of finding a common denominator is already complete.

At this point, we can make use of the algebraic property that $\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$, for any numbers $a , b$, and $c , c \ne 0$.

Thus we have

$\frac{9 a - 11 x}{8 a} - \frac{2 a - 7 x}{8 a}$
$= \frac{\left(9 a - 11 x\right) - \left(2 a - 7 x\right)}{8 a}$
$= \frac{9 a - 11 x - 2 a + 7 x}{8 a}$
$= \frac{7 a - 4 x}{8 a}$

There is no further meaningful way to simplify this answer, so we are done. Do note, however, that just as we can combine terms with common denominators, we can also break them apart. See that:

$\frac{7 a - 4 x}{8 a} = \frac{7 a}{8 a} - \frac{4 x}{8 a} = \frac{7}{8} - \frac{x}{2 a}$