Find the LCD, convert each fraction, add or subtract numerators, then simplify the result.
x+2, x^2-1, 2x-3LCD = product of all unique factors (highest power each)
Step 1: Factor every denominator completely — look for linear factors like (x + 3) or (x − 2) and quadratics like (x² − 1) = (x + 1)(x − 1).
Step 2: The LCD is built from every unique factor, each raised to its highest power across all denominators.
Step 3: Multiply each fraction top and bottom by whatever is missing to reach the LCD denominator. This creates equivalent fractions with a common denominator.
Step 4: Combine the numerators (keeping the LCD as the denominator), then simplify by combining like terms and canceling common factors.
a/b − c/d = (a·lcd_factor − c·lcd_factor) / LCD
For subtraction, the negative sign must be distributed across the ENTIRE second numerator before combining. This is the single most common error students make.
Wrong: x/(x−1) − (x+2)/(x+1) → numerator: x − x + 2 ✗
Right: x/(x−1) − (x+2)/(x+1) → numerator: x(x+1) − (x+2)(x−1) = x²+x − (x²+x−2) = 2 ✓
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