Multiplying and Dividing Rational Expressions
Simplify rational expressions by factoring polynomials first, then canceling common factors before multiplying. Master algebraic fraction operations in Grade 9 algebra.
Key Concepts
New Concept If $a$, $b$, $c$, and $d$ are nonzero polynomials, then $\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$. What’s next Next, you’ll apply these rules to multiply, divide, and simplify expressions involving polynomials, just as you would with regular fractions.
Common Questions
What is the first step when multiplying rational expressions?
Factor all polynomials in numerators and denominators completely before multiplying. This lets you cancel common factors and keep the expression simple.
How do you divide rational expressions?
Multiply by the reciprocal: flip the second fraction, then multiply. Factor everything first, cancel common factors, then multiply straight across.
Why must you factor before canceling in rational expressions?
You can only cancel entire factors, not individual terms. In (x+5)(x-3)/[(x-3)(x+3)], you can cancel (x-3) but cannot cancel individual x terms across addition.