Chapter 11.2, Problem 24PPE

To determine

Multiply: $\frac{2m+1}{3m-6}·(9m^2-36)$

Answer to Problem 24PPE

  $\frac{2m+1}{3m-6}·(9m^2-36)=4(t^2+3t+2)$

Explanation of Solution

Given:

Multiply: $\frac{2m+1}{3m-6}·(9m^2-36)$

Concept Used:

For multiplication of rational expression, we always cancel the common factor from numerator and denominator and if necessary multiply the numerators and denominators separately.

Calculation:

  $\begin{array}{l}\frac{2m+1}{3m-6}·(9m^2-36)\\ \frac{2m+1}{3(m-2)}·9(m^2-4)\\ \frac{2m+1}{3(m-2)}·3·3(m+2)(m-2)=\frac{m-2}{m-2}·\frac{3}{3}·3·(2m+1)(m+2)\\ 3(2m+1)(m+2)=3(2m^2+5m+2)\end{array}$

Thus, $\frac{2m+1}{3m-6}·(9m^2-36)=4(t^2+3t+2)$