Question

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

Answer 1

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

`4a^2-1=0`
`4a^2=1`
`a^2=1/4`
`a^2=+-1/2`, thus the factors are `(2a-1)=0` and `(2a+1)=0`

`a^2-4=0`
`a^2=4`
`a=+-2`, thus the factors are `(a-2)=0` and `(a+2)=0`

Rewriting:

`(cancel(2a-1)(2a+1))/(cancel(a-2)(a+2))cancel(a-2)/cancel(2a-1)`

Final answer: `(2a+1)/(a+2)`