Question

HELP PLEASE!! I DONT UNDERSTAND!!!!!!!!!! THANKS SO MUCH

Answer 1

Hello, please consider the following.

We will multiply the numerator and denominator by

`4+√(6x)`

to get rid of the root in the denominator.

First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.

`4-√(6x) =0<=>√(6x)=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=(16)/(6)=(8)/(3)`

We need to take any x real number different from 8/3 then and simplify the expression.

Let's do it!

`\begin{aligned}(4)/(4-√(6x))&=(4(4+√(6x)))/((4+√(6x))(4-√(6x)))\\\\&=(4(4+√(6x)))/((4^2-√(6x)^2))\\\\&=(4(4+√(6x)))/((16-6x))\\\\&=(2(4+√(6x)))/((8-3x))\\\\&\large \boxed{=(8+2√(6x))/(8-3x)}\end{aligned}`

Thank you