# Multiplying and Dividing Rational Expressions

In this video, we are going to multiply and divide rational expressions.

We can start by either directly perform the operation or reduce across.

For example: $\frac{15}{4}\times\frac{32}{20}$

First, reduce the numbers that are across from each other
$\frac{15}{4}\times\frac{32}{20}$
$\frac{3}{1}\times\frac{8}{4}$

Further reduce, which can be done vertically with the 8 and the 4
$\frac{3}{1}\times\frac{2}{1}$

Multiply
$\frac{6}{1}$

And we have
$6$

With variables, it is the same concept
$\frac{3x+15}{x^2+7x+12}\times\frac{x^2-9}{x+5}$

Factor the expressions if necessary
$\frac{3(x+5)}{(x+4)(x+3)}\times\frac{(x+3)(x+3)}{(x+5)}$

Reduce diagonally
$\frac{3}{(x+4)}\times\frac{(x+3)}{1}$

Multiple across
$\frac{3(x+3)}{x+4}$

Division is similar to multiplication.
Remember to Keep, Change, Flip

For example: $\frac{x+8}{3x}\div\frac{4x+32}{15x^4}$

Keep the first fraction, change the operation from division to multiplication, and flip the second fraction
$\frac{x+8}{3x}\times\frac{15x^4}{4x+32}$

Factor if necessary
$\frac{x+8}{3x}\times\frac{15x^4}{4(x+8)}$

Reduce expressions
$\frac{1}{1}\times\frac{5x^3}{4}$

Multiply across
$\frac{5x^3}{4}$

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Used by students across the country. Pre-Algebra, Algebra I, Geometry, & Algebra II