Multiplication and Division of Fractions.

Find quotient of $\frac{a b}{(a - b)^{2}} \div \frac{a c}{a^{2} - b^{2}}$ .

$\frac{a b}{(a - b)^{2}} \div \frac{a c}{a^{2} - b^{2}} & = \frac{a b}{(a - b) (a - b)} \times \frac{(a - b) (a + b)}{a c} & = \frac{b (a + b)}{c (a - b)} .$

Find the result of $\frac{1}{x} \times \frac{x^{2} - 1}{x^{2} - 4 x - 5} \div \frac{x^{2} + 2 x - 3}{x^{2} - 25}$ .

$& \frac{1}{x} \times \frac{x^{2} - 1}{x^{2} - 4 x - 5} \div \frac{x^{2} + 2 x - 3}{x^{2} - 25} & = \frac{1}{x} \times \frac{x^{2} - 1}{x^{2} - 4 x - 5} \times \frac{x^{2} - 25}{x^{2} + 2 x - 3} & = \frac{1}{x} \times \frac{(x - 1) (x + 1)}{(x - 5) (x + 1)} \times \frac{(x - 5) (x + 5)}{(x + 3) (x - 1)} & = \frac{x + 5}{x (x + 3)} .$

Exercise 49.

Express in the simplest form:

$\frac{15 a^{2}}{7 b^{2}} \times \frac{28 a b}{9 a^{3} c}$ .

$\frac{3 x^{2} y^{2} z^{3}}{4 a^{2} b^{2} c^{2}} \times \frac{8 a^{3} b^{2} c^{2}}{9 x^{2} y z^{3}}$ .

$\frac{5 m^{2} n^{2} p^{4}}{3 x^{2} y z^{3}} \times \frac{21 x y z^{2}}{20 m^{2} n^{2} p^{2}}$ .

$\frac{16 a^{4} b^{2} c^{3}}{21 m^{2} x^{3} y^{4}} \times \frac{3 m^{3} x^{3} y^{4}}{8 a^{2} b^{2} c^{2}}$ .

$\frac{2 a}{b c} \times \frac{3 b}{a c} \times \frac{5 c}{a b}$ .

$\frac{2 a^{3}}{3 b c} \times \frac{3 b^{3}}{5 a c} \times \frac{5 c^{3}}{2 a b}$ .

$\frac{5 a b c^{3}}{3 x^{2}} \div \frac{10 a c^{3}}{6 b x^{2}}$ .

$\frac{x^{2} - a^{2}}{x^{2} - 4 a^{2}} \times \frac{x + 2 a}{x - a}$ .

$\frac{x^{2} y^{2} + 3 x y}{4 c^{2} - 1} \times \frac{2 c + 1}{x y + 3}$ .

$\frac{a^{2} - 100}{a^{2} - 9} \times \frac{a - 3}{a - 10}$ .

$\frac{9 x^{2} - 4 y^{2}}{x^{2} - 4} \times \frac{x + 2}{3 x - 2 y}$ .

$\frac{25 a^{2} - b^{2}}{16 a^{2} - 9 b^{2}} \div \frac{5 a - b}{4 a - 3 b}$ .

$\frac{x^{2} - 49}{(a + b)^{2} - c^{2}} \div \frac{x + 7}{(a + b) - c}$ .

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