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

May 23, 2015

$\frac{5 x + 2}{5 x} \cdot \left(\frac{25 {x}^{2}}{25 {x}^{2} - 4}\right)$

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

so,
$25 {x}^{2} - 4 = {\left(5 x\right)}^{2} - {\left(2\right)}^{2} = \left(5 x + 2\right) \left(5 x - 2\right)$

the expression can be written as:
$\frac{\cancel{5 x + 2}}{\left(5 x\right)} \cdot \frac{25 {x}^{2}}{\cancel{5 x + 2} \left(5 x - 2\right)}$

$= \frac{25 {x}^{2}}{\left(5 x\right) \left(5 x - 2\right)}$

$= \frac{5 x}{5 x - 2}$