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

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Answer 1 · 2015-07-29T12:55:50

Your only option is to rationalize the denominator.

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

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

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