Question

How do you simplify `(x+3)/sqrt(9x^2+5x)`?

Answer 1

Your only option is to rationalize the denominator.

Explanation:

The only option you have for trying to simplify this expression is to rationalize the denominator by multiplying the fraction by

`sqrt(9x^2 + 5x)/sqrt(9x^2 + 5x)`

This will get you

`(x+3)/(sqrt(9x^2 + 5x)) * sqrt(9x^2 + 5x)/sqrt(9x^2 + 5x) = ((x + 3) * sqrt(9x^2 + 5x))/(sqrt(9x^2 + 5x) * sqrt(9x^2 + 5x))`

The denominator will now have the form

`color(blue)(sqrt(x) * sqrt(x) = sqrt(x^2) = x)`

which means that you have

`((x + 3) * sqrt(9x^2 + 5x))/(9x^2 + 5x) = color(green)((x + 3)/x * sqrt(9x^2 + 5x)/(9x + 5)`