Adding and Subtracting Rational Expressions Math Example 1

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

Example 1

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

Solution

  1. 1
    Step 1: LCD = (x+1)(x−2)(x+1)(x-2).
  2. 2
    Step 2: 2(x−2)(x+1)(x−2)+3(x+1)(x+1)(x−2)\frac{2(x-2)}{(x+1)(x-2)} + \frac{3(x+1)}{(x+1)(x-2)}.
  3. 3
    Step 3: Combine: 2x−4+3x+3(x+1)(x−2)=5x−1(x+1)(x−2)\frac{2x - 4 + 3x + 3}{(x+1)(x-2)} = \frac{5x - 1}{(x+1)(x-2)}.
  4. 4
    Check: At x=3x = 3: 24+31=72\frac{2}{4} + \frac{3}{1} = \frac{7}{2} and 144=72\frac{14}{4} = \frac{7}{2} ✓

Answer

5x−1(x+1)(x−2)\frac{5x - 1}{(x+1)(x-2)}
To add rational expressions with different denominators, find the LCD, rewrite each fraction with the LCD, then combine numerators. This mirrors adding numeric fractions.

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 2 hard

Subtract [formula].

Example 3 easy

Add [formula].

Example 4 medium

Subtract [formula].

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