# Adding and Subtracting Rational Expressions

## Part 1

In the first video, we are going to add and subtract simple rational expressions.

For example: $\frac{3}{2x}+\frac{5}{2x}$

Simply combine the numerator and the denominator together if the denominators are the same and we have
$\frac{8}{2x}$

Let’s look at another example: $\frac{2}{6n}+\frac{4}{2mn}$

Since the denominators are not the same, multiple each fraction to achieve the least common multiple
$\frac{(m)2}{(m)6n}+\frac{(3)4}{(3)2mn}$
$\frac{2m}{6mn}+\frac{12}{6mn}$

Now, we can add the terms together
$\frac{2m+12}{6mn}$

In order to reduce the expression, factor if necessary
$\frac{2(m+6)}{6mn}$

Reduce, and our final answer is
$\frac{(m+6)}{3mn}$

## Part 2

In the second video, we are going to add and subtract more complex rational expressions.

For example: $\frac{6}{n-6}+\frac{3}{n-1}$

Multiply each fraction to achieve the least common multiple
$\frac{(n-1)6}{(n-1)(n-6)}+\frac{(n-6)3}{(n-6)(n-1)}$

Use the distributive property to multiply
$\frac{6n-6}{(n-1)(n-6)}+\frac{3n-8}{(n-1)(n-6)}$

Now that we have common denominators, add the numerators together
$\frac{9n-24}{(n-1)(n-6)}$

Factor any expression if necessary
$\frac{3(3n-8)}{(n-1)(n-6)}$

Since nothing can be reduced, we are going back to the original expression
$\frac{9n-24}{(n-1)(n-6)}$

Use FOIL (First, Outside, Inside, Last) to multiply
$\frac{9n-24}{n^2-6n-n+6}$

Combine like terms, and we have
$\frac{9n-24}{n^2-7n+6}$

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