Adding and Subtracting Rational Expressions Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium
Subtract 5x−3−2x+1\frac{5}{x-3} - \frac{2}{x+1}.

Solution

  1. 1
    LCD = (x−3)(x+1)(x-3)(x+1). 5(x+1)−2(x−3)(x−3)(x+1)=5x+5−2x+6(x−3)(x+1)\frac{5(x+1) - 2(x-3)}{(x-3)(x+1)} = \frac{5x+5-2x+6}{(x-3)(x+1)}.
  2. 2
    =3x+11(x−3)(x+1)= \frac{3x + 11}{(x-3)(x+1)}.

Answer

3x+11(x−3)(x+1)\frac{3x + 11}{(x-3)(x+1)}
When subtracting, distribute the negative to the entire second numerator: −2(x−3)=−2x+6-2(x-3) = -2x + 6. A common error is writing −2x−6-2x - 6 instead.

About Adding and Subtracting Rational Expressions

Adding or subtracting rational expressions by finding a least common denominator (LCD), rewriting each fraction with the LCD, then combining the numerators over the common denominator.

Learn more about Adding and Subtracting Rational Expressions →

More Adding and Subtracting Rational Expressions Examples

Example 1 medium

Add [formula].

Example 2 hard

Subtract [formula].

Example 3 easy

Add [formula].

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