Question B.5.4: Dividing rational expressions Perform the indicated operatio...
Dividing rational expressions
Perform the indicated operations.
a. \frac{9}{2 x} \div \frac{3}{x} b. \frac{4-x^{2}}{6} \div \frac{x-2}{2}
a. \frac{9}{2 x} \div \frac{3}{x}=\frac{9}{2 x} \cdot \frac{x}{3} Invert and multiply.
=\frac{3 \cdot 3}{2 x} \cdot \frac{x}{3} Factor completely.
=\frac{3}{2} Divide out common factors.
b. \frac{4-x^{2}}{6} \div \frac{x-2}{2}=\frac{-1(x-2)(x+2)}{2 \cdot 3} \cdot \frac{2}{x-2} Invert and multiply
=\frac{-x-2}{3} Divide out common factors.
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