Solving Rational Equations

By Judith F, Cheryl N, & Elaine V

What is a rational equation?

An equation where a variable occurs in the denominator of a rational expression

Simplest example: 1

x

Steps to Solving:1. Identify the values which will result in no

solution (find the values of x which will make the denominator equal 0)

2. Identify the LCD (Lowest Common Denominator),

3. Multiply both sides of the equation by the LCD

4. Solve the numerators, and reject any results which provide no solution

Now try it!

X-1 = 2 15 = 5

Multiply both sides by the LCD, which happens to be 15

X-1 = (2)(3)

15 = (5)(3)

X-1 = 6

15 = 15

X-1 = 6

+ 1 +1

X = 7

Let’s make it a little harder!

X = 0, -2

LCD = 5x(x+2)

And yet another example:X = 0, 2

The LCD is: x(x-2)

Crazy Complexity!

For this example you’re going to have to use Ernie’s favourite “F” word…