1. ## Probably a simple radical subtraction but making sure...

It goes like this:

x(square root of 5x-1) - (square root of 5x-1)

They are like terms now. Is it something like this:

x - (square root of 5x-1) ?

2. Actually, what you're going to do is factor the $\displaystyle \sqrt{5x-1}$ out of the equation, what you do is:

1. Pull the $\displaystyle \sqrt{5x-1}$ out by adding parentheses around the entire equation and tacking a $\displaystyle \sqrt{5x-1}$ right before the first parenthesis:

Original:

$\displaystyle x\sqrt{5x-1} - \sqrt{5x-1}$

Step 1:

$\displaystyle \sqrt{5x-1}(x\sqrt{5x-1} - \sqrt{5x-1})$

2. Inside the parentheses, you divide each term by $\displaystyle \sqrt{5x-1}$:

Step 1:

$\displaystyle \sqrt{5x-1}(x\sqrt{5x-1} - \sqrt{5x-1})$

Step 2:

$\displaystyle \sqrt{5x-1}(x - 1)$

And with that, you are done.

3. Ok, that makes sense, but it's also all divided by 5. So am I still able to do that if there is a 5 on the bottom?

4. Hello, cjh824!

Simplify: .$\displaystyle x\sqrt{5x-1} - \sqrt{5x-1}$

We have: . $\displaystyle x\text{(thing)} - \text{(thing)}\quad\hdots \text{ or: }\:xa - a$

$\displaystyle \text{Factor out the }a.$