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

1 Answer
Jul 29, 2015

Answer:

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)#