Multiplying and Dividing

Algebra 1 · Axiom Academy

LESSON Multiplying and Dividing Rational Expressions The rules for multiplying and dividing fractions carry straight over to algebra — and factoring first makes the work collapse. 1. Multiplying Fractions: Straight Across Start where you're already comfortable. To multiply two fractions you multiply the numerators together for the new top, and the denominators together for the new bottom. Nothing flips, nothing lines up — it's straight across. tops multiply to the new top, bottoms to the new bottom 2. The Same Rule, Now with Polynomials Swap the numbers for polynomials and the rule is identical — multiply tops, multiply bottoms. But now watch for a shared factor : an x on a top and an x on a bottom cancel to 1 , exactly like a shared number would. where A,B,C,D are polynomials and (you can't divide by zero). 3. Factor First — Then the Cancelling Appears Most shared factors are hidden until you factor. x^2-9 doesn't obviously share anything with x-3 — but factored as (x-3)(x+3) , the (x-3) is suddenly right there to cancel. So the order is always the same: factor everything, cancel matches, multiply what's left. 4. Division: Flip the Second Fraction Dividing is multiplying in disguise. To divide by a fraction, flip the second one to its reciprocal and switch the to a . Then it's an ordinary multiplication: factor, cancel, multiply. Keep the first fraction, change to , and flip the second. Flip the second fraction and multiply:

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