Question

Rationalize the denominator

Answer 1

\[\frac{\sqrt{x^2}}{\sqrt{x+1}}\]

Answer 2

Square that thing.

Answer 3

\[\frac{\sqrt{x^3+x^2}}{x+1}\]

Answer 4

\[\frac{\sqrt{x^2}}{\sqrt{x+1}}=\frac{x}{\sqrt{x+1}}=\frac{x(\sqrt{x+1})}{(\sqrt{x+1)^2}} = \frac{x\sqrt{x+1}}{x+1}\]

Answer 5

^

Answer 6

I don't understand what you did to the numerator.

Answer 7

In case you need to multiply the numerator\[= \frac{\sqrt{x^2(x+1)}}{x+1}= \frac{\sqrt{x^3+x^2}}{x+1}\]

Answer 8

I need to...?

Answer 9

Ahh... bad typing.. I was multiplying the conjugate 'sqrt(x+1)'

Answer 10

\(\huge \frac{\sqrt{x^2}*\sqrt{x+1}}{\sqrt{x+1}*\sqrt{x+1}}=\frac{x\sqrt{x+1}}{x+1}\)

Answer 11

\[\frac{\sqrt{x^2}}{\sqrt{x+1}}=\frac{x}{\sqrt{x+1}}=\frac{x(\sqrt{x+1})}{(\sqrt{x+1})(\sqrt{x+1})} = \frac{x\sqrt{x+1}}{x+1}\]\[ = \frac{\sqrt{x^2(x+1)}}{x+1}= \frac{\sqrt{x^3+x^2}}{x+1}\]That's what you've got

Answer 12

Okay!!! I am still contemplating whether or not I should leave it that way but thank you so much for all your help @zepp and @RolyPoly

Answer 13

You are welcome :)