Express $\frac{2}{x + 3} - \frac{1}{x - 2}$ as a simple fraction

Step 1: Analyze the question We need to combine two fractions with different denominators into one fraction.

Step 2: Concept Use the common denominator (x + 3)(x − 2).

Step 3: Solution

Expand the numerator:

• 2(x − 2) = 2x − 4
• 1(x + 3) = x + 3

Numerator: 2x − 4 − x − 3 = x − 7

Expand the denominator: (x + 3)(x − 2) = x² − 2x + 3x − 6 = x² + x − 6

Step 4: Answer

Tip: When subtracting fractions, put the minus sign in front of the whole second numerator. Many students forget to change the sign of the 3 in (x + 3), writing 2x − 4 − x + 3 instead of 2x − 4 − x − 3. Use brackets to avoid this error.