One of the things we learned this week in Precalc 11 is how to solve rational equations.

#### Cross-Multiplying

The cross-multiplying method only works if a fraction is equal to another fraction () and does not work with 3 or more terms ()

#### Examples

Solve:

First we need to determine the non-permissible values for x.

Next, cross-multiply. Multiply the numerator for the first fraction to the denominator for the second one, vice versa with the denominator for the first fraction.

Then distribute.

Since there is a square, we know that it’s a quadratic and it has 2 possible solutions. Move all the terms on one side.

Since we it doesn’t factor with nice numbers we can use the quadratic formula.

Solve:

#### Converting to a common denominator

Works everytime even with 3 or more terms.

##### Example

Solve:

First determine the non-permissible values.

Then determine the Lowest/Least Common Denominator (LCD). LCD=2x

Then multiply the fractions so that they have the same denominators.

Since the denominators are all the same the numerators also have to be the same, so we could ignore the denominators.

Since it’s a quadratic we have to make it equal 0 and then factor.