EDGE Math 8

Simplest Form of Rational Expressions

Simplifying rational expressions is similar to reducing fractions like $\frac{42}{54}$ to lowest terms. First, factor both the numerator and the denominator. Then write the fraction as a product of two fractions.

\frac{42}{54} = \frac{7 \cdot 6}{9 \cdot 6} = \frac{7}{9} \cdot \frac{6}{6}

Since $\frac{6}{6} = 1,$ the right-hand side of the equation becomes

\frac{7}{9} \cdot \frac{6}{6} = \frac{7}{9} \cdot 1 = \frac{7}{9} .

Since $\frac{7}{9}$ cannot be reduced to lowest terms anymore, you can say that $\frac{42}{54} = \frac{7}{9} .$