Mathematics » Rational Expressions and Equations » Add and Subtract Rational Expressions with Unlike Denominators

# Finding Equivalent Rational Expressions

## Finding Equivalent Rational Expressions

When we add numerical fractions, once we find the LCD, we rewrite each fraction as an equivalent fraction with the LCD.

We will do the same thing for rational expressions.

## Example

Rewrite as equivalent rational expressions with denominator $$\left(x+1\right)\left(x-3\right)\left(x+3\right)$$: $$\frac{8}{{x}^{2}-2x-3},\frac{3x}{{x}^{2}+4x+3}.$$

### Solution

 Factor each denominator. Find the LCD. Multiply each denominator by the ‘missing’ factor and multiply each numerator by the same factor. Simplify the numerators.