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Subtracting
Subtract two fractions with unlike denominators by finding the LCD and converting to equivalent fractions:
Step 1 — Find the LCD and rewrite: Factor each denominator: and . The LCD is . The denominator is missing three factors of (i.e., ), and the denominator is missing the factor . Multiply accordingly:
Step 2 — Subtract: Combine the numerators: .
Step 3 — Simplify: Both and share the factor . Dividing each by gives , which is written as .
When the first numerator is smaller than the second after conversion, the result is negative. As with addition, never simplify the equivalent fractions before subtracting — that would destroy the common denominator.
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