Multiply, divide, add and subtract rational expressions

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Learn it Factor everything first. To multiply, cancel common factors; to divide, multiply by the reciprocal. To add or subtract, use a common denominator. Always state restrictions: values that make any original denominator (or a divisor) zero.

Example: Simplify (x² − 9)/(x² + 5x + 6) ÷ (x − 3)/(x + 2).

Multiply by the reciprocal: (x − 3)(x + 3)/[(x + 2)(x + 3)] × (x + 2)/(x − 3).
Everything cancels: 1, with x ≠ −3, −2, 3.

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