Question

How do you multiply `(5x+2)/(5x)*(25x^2)/(25x^2-4)`?

Answer 1

`(5x+2)/(5x)*((25x^2)/(25x^2-4))`

We know that `color(blue)(a^2 - b^2 = (a+b)(a-b)`

so,
`25x^2-4 =(5x)^2 - (2)^2= (5x+2)(5x-2)`

the expression can be written as:
`(cancel(5x+2))/((5x))*(25x^2)/(cancel(5x+2)(5x-2))`

`= (25x^2)/((5x)(5x-2))`

`= (5x)/(5x-2)`