AI Tutor
If you had to multiply 23Γ—910\frac{2}{3} \times \frac{9}{10}, would you multiply first to get 1830\frac{18}{30} and reduce, or cross-cancel first to find 35\frac{3}{5} in two seconds?
With algebraic fractions, multiplying everything out first creates massive polynomial nightmares. Factoring and canceling common factors before multiplying is the secret superpower.
Why does this work with variables too?

The Fraction Multiplication Rule

A rational expression is simply a fraction whose numerator and denominator are polynomials, like P(x)Q(x)\frac{P(x)}{Q(x)} where Q(x)β‰ 0Q(x) \neq 0.
Because multiplication is commutative (aβ‹…c=cβ‹…aa \cdot c = c \cdot a), multiplying two fractions merges them into one single fraction: ABβ‹…CD=Aβ‹…CBβ‹…D\frac{A}{B} \cdot \frac{C}{D} = \frac{A \cdot C}{B \cdot D}.
You can divide out common multiplicative factors shared between any numerator and any denominator using the Identity Property of Multiplication: Aβ‹…CBβ‹…C=ABβ‹…CC=ABβ‹…1=AB\frac{A \cdot C}{B \cdot C} = \frac{A}{B} \cdot \frac{C}{C} = \frac{A}{B} \cdot 1 = \frac{A}{B}.
Ready to see this strategy handle quadratic expressions step-by-step?

Step-by-Step Multiplication

Let's multiply x2βˆ’9x2+5x+6β‹…x+2xβˆ’3\frac{x^2 - 9}{x^2 + 5x + 6} \cdot \frac{x + 2}{x - 3}.
First, factor all numerators and denominators completely into linear factors.