# How do you multiply (4a^2 - 1) /( a^2 - 4) * (a - 2)/(2a - 1)?

May 23, 2015

Before multiplying we can factor the two quadratic equations you got there:

$4 {a}^{2} - 1 = 0$
$4 {a}^{2} = 1$
${a}^{2} = \frac{1}{4}$
${a}^{2} = \pm \frac{1}{2}$, thus the factors are $\left(2 a - 1\right) = 0$ and $\left(2 a + 1\right) = 0$

${a}^{2} - 4 = 0$
${a}^{2} = 4$
$a = \pm 2$, thus the factors are $\left(a - 2\right) = 0$ and $\left(a + 2\right) = 0$

Rewriting:

$\frac{\cancel{2 a - 1} \left(2 a + 1\right)}{\cancel{a - 2} \left(a + 2\right)} \frac{\cancel{a - 2}}{\cancel{2 a - 1}}$

Final answer: $\frac{2 a + 1}{a + 2}$