1) $\frac{1}{x - 1} \times \frac{8x - 8}{8} = \frac{1}{x - 1} \times \frac{8(x - 1)}{8} = \frac{8(x - 1)}{8(x - 1)} = 1$
2) $\frac{2y - 5}{(y + 2)(y - 3)} \times \frac{y - 3}{4y - 10} = \frac{2y - 5}{(y + 2)(y - 3)} \times \frac{y - 3}{2(2y - 5)} = \frac{(2y - 5)(y - 3)}{2(y + 2)(y - 3)(2y - 5)} = \frac{1}{2(y + 2)}$
3) $\frac{3x - 9y}{x^2 - xy} \div \frac{x^2 - 9y^2}{x^2 - y^2} = \frac{3(x - 3y)}{x(x - y)} \times \frac{(x - y)(x + y)}{(x - 3y)(x + 3y)} = \frac{3(x - 3y)(x - y)(x + y)}{x(x - y)(x - 3y)(x + 3y)} = \frac{3(x + y)}{x(x + 3y)}$
4) $\frac{r - 2}{8r + 16} \times \frac{r + 2}{r^2 - 2r} = \frac{r - 2}{8(r + 2)} \times \frac{r + 2}{r(r - 2)} = \frac{(r - 2)(r + 2)}{8(r + 2)r(r - 2)} = \frac{1}{8r}$
5) $\frac{1}{p - 4} \div \frac{3p}{4p - 16} = \frac{1}{p - 4} \times \frac{4p - 16}{3p} = \frac{1}{p - 4} \times \frac{4(p - 4)}{3p} = \frac{4(p - 4)}{3p(p - 4)} = \frac{4}{3p}$
6) $\frac{x^3 + 2x^2}{y^3 - y} \times \frac{y^2 - 1}{x^2 - 4} = \frac{x^2(x + 2)}{y(y^2 - 1)} \times \frac{(y - 1)(y + 1)}{(x - 2)(x + 2)} = \frac{x^2(x + 2)(y - 1)(y + 1)}{y(y - 1)(y + 1)(x - 2)(x + 2)} = \frac{x^2}{y(x - 2)}$
7) $\frac{5b^2c^2}{10bc} \div \frac{6b^2c}{2c^2} = \frac{5b^2c^2}{10bc} \times \frac{2c^2}{6b^2c} = \frac{5b^2c^2 \cdot 2c^2}{10bc \cdot 6b^2c} = \frac{10b^2c^4}{60b^3c^2} = \frac{c^2}{6b}$
8) $\frac{2p}{q} \div \frac{4p}{q^2} = \frac{2p}{q} \times \frac{q^2}{4p} = \frac{2p \cdot q^2}{q \cdot 4p} = \frac{2pq^2}{4pq} = \frac{q}{2}$
Parent Tip: Review the logic above to help your child master the concept of algebraic expression worksheet.
