# Addition and Subtraction of Rational Expressions

## Key Questions

• You can keep the same denominator and add or subtract the numerators.

$\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}$ and $\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}$

I hope that this was helpful.

• The least common denominator is the least common multiple of denominators.

Example
Find the least common denominator to compute:

$\frac{1}{3} + \frac{1}{4} - \frac{1}{6}$

Let us observe:

Multiples of $3$: $3 , 6 , 9$, 12,$15 , \ldots$
Multiples of $4$: $4 , 8$,12, $16 , \ldots$
Multiples of $6$: $6$,12,$18 , \ldots$,

So, the least common multiple of $3$,$4$, and $6$ is $12$.

Hence,

$\frac{1}{3} + \frac{1}{4} - \frac{1}{6} = \frac{4}{12} + \frac{3}{12} - \frac{2}{6} = \frac{4 + 3 - 2}{12} = \frac{5}{12}$
...
I hope that this was helpful.

• You need to put each term over a common denominator by multiplying each term by the appropriate form of $1$ or $\frac{n}{n}$

• $\frac{A}{B} + \frac{C}{D} = \frac{A D + B C}{B D}$

and

$\frac{A}{B} - \frac{C}{D} = \frac{A D - B C}{B D}$