Rational Expressions • Topic 2 of 6

Multiplication

To multiply rational expressions, multiply numerators together and denominators together, but factor and cancel common factors first to keep the work small. So (x/3)(6/x²) = 6x/(3x²) = 2/x. When numerators and denominators share factors across the two fractions, cancel them before multiplying — (x + 2)/4 · 8/(x + 2) cancels the (x + 2) and gives 8/4 = 2. No common denominator is needed for multiplication. Always note restrictions from every denominator. This is one of the cleaner rational operations and a frequent SAT simplification step.

✅ Solved examples

1. Simplify (x/3)(6/x²).
6x/(3x²) = 2/x.
2. Simplify (2/x)(x²/6).
2x²/(6x) = x/3.
3. Simplify (x + 1)/4 · 8/(x + 1).
Cancel (x + 1): 8/4 = 2.
4. Simplify (3/x)(x/9).
3x/(9x) = 1/3.

✏️ Practice — try these, take hints as needed

1. Simplify (x/4)(8/x).
Multiply across: 8x/(4x).
Cancel x.
—
2.
2. Simplify (5/x)(x²/10).
5x²/(10x).
Reduce.
—
x/2.
3. Simplify (x − 2)/3 · 6/(x − 2).
Cancel (x − 2).
6/3.
—
2.
4. Simplify (2/x)(x/7).
2x/(7x).
Cancel x.
—
2/7.
5. Simplify (x²/2)(4/x).
4x²/(2x).
Reduce.
—
2x.

📝 Topic test — 8 questions

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