EDGE Math 8

Example 4

Divide and then simplify if possible.

\frac{16 a + 32}{5 a - 15} \div \frac{24 a + 48}{4 a - 12}

Solution

\frac{16 a + 32}{5 a - 15} \div \frac{24 a + 48}{4 a - 12}

= \frac{16 a + 32}{5 a - 15} \cdot \frac{4 a - 12}{24 a + 48}

= \frac{(16 a + 32) (4 a - 12)}{(5 a - 15) (24 a + 48)}

Factor the expressions in the numerator and the denominator. Then cancel common factors.

\frac{(16 a + 32) (4 a - 12)}{(5 a - 15) (24 a + 48)}

= \frac{16 (a + 2) (4) (a - 3)}{5 (a - 3) (24) (a + 2)}

= \frac{8}{15}

Thus,

\frac{16 a + 32}{5 a - 15} \div \frac{24 a + 48}{4 a - 12} = \frac{8}{15} .