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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}