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.

The above image shows how to find the LCD (least common denominator) when adding numerical fractions in the example seven-twelfths plus five-eighteenths. The image shows 7 times 3 divided by 12 times 3 plus 5 times 2 plus 18 times 2. Below this is 21 divided by 36 plus 10 divided by 36. The image next to this shows that 12 equals 2 times 2 times 3. Below this shows 18 equals 2 times 3 times 3. A line is drawn. Below it is LCD equals 2 times 2 times 3 times 3. The line below this shows that the LCD equals 36.

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..

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