When we add or subtract two fractions, they must have the same denominator.

We can multiply a complete equation by a lowest common denominator to "get rid of" all denominators, making the equation easier to solve.

**Example**

Simplify the following equation to one that is quadratic:

2 | + | 3 | = | 4 |

x - 1 | x + 2 |

**Answer**

We multiply the whole equation by (x - 1) (x + 2).

This gives us:

2 (x + 2) + 3 (x - 1) = 4 (x - 1) (x + 2)

Simplify to get:

2x + 4 + 3x - 3 = 4 (x^{2} + x - 2)

5x + 1 = 4x^{2} + 4x - 8

4x^{2} + 4x - 8 - 5x - 1 = 0

**4x ^{2} - x - 9 = 0**

This can now be solved using the quadratic formula, but for this worksheet we just need to arrive at this quadratic equation in the form ax^{2} + bx + c = 0