Adding and Subtracting Rational Expressions Math Example 2

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

Example 2

hard
Subtract xx+2−3x2+4x+4\frac{x}{x+2} - \frac{3}{x^2 + 4x + 4}.

Solution

  1. 1
    Step 1: Factor: x2+4x+4=(x+2)2x^2 + 4x + 4 = (x+2)^2. LCD = (x+2)2(x+2)^2.
  2. 2
    Step 2: x(x+2)(x+2)2−3(x+2)2\frac{x(x+2)}{(x+2)^2} - \frac{3}{(x+2)^2}.
  3. 3
    Step 3: Combine: x2+2x−3(x+2)2=(x+3)(x−1)(x+2)2\frac{x^2 + 2x - 3}{(x+2)^2} = \frac{(x+3)(x-1)}{(x+2)^2}.
  4. 4
    Check: At x=1x = 1: 13−39=13−13=0\frac{1}{3} - \frac{3}{9} = \frac{1}{3} - \frac{1}{3} = 0 and 4⋅09=0\frac{4 \cdot 0}{9} = 0 ✓

Answer

(x+3)(x−1)(x+2)2\frac{(x+3)(x-1)}{(x+2)^2}
When one denominator is a factor of the other, the LCD is the higher-power denominator. After combining, try to factor the numerator for a fully simplified answer.

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 3 easy

Add [formula].

Example 4 medium

Subtract [formula].

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