simplify the expression

(4 square root of x)/(6-square root of x)

I need help with this. I've worked it out to the point where i got (2 square root of x)/(3-square root of x), but I'm pretty sure that it can be simplified further. If what I'm thinking is right you have to cancel out the X's and work out the regular numbers which would then give you the simplest form.

See previous post: Tue, 8-25-15, 2:55 PM.

To simplify the expression (4√x) / (6 - √x), you are on the right track.

Here's how you can simplify it further:
1. Simplify the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of (6 - √x) is (6 + √x). This will eliminate the square root from the denominator.

(4√x) / (6 - √x) * (6 + √x) / (6 + √x)

2. Simplify by using the distributive property to expand the numerator.

(4√x * 6 + 4√x * √x) / (6 * 6 + 6 * √x - 6 * √x - (√x) * (√x))

3. Simplify further by multiplying across.

(24√x + 4x) / (36 + √x^2 - √x^2)

4. Notice that √x^2 simplifies to x, so the expression becomes:

(24√x + 4x) / (36 + x - x)

5. Simplify even further by canceling out the x terms:

(24√x + 4x) / 36

6. You can simplify this fraction by dividing both the numerator and the denominator by the greatest common divisor, which is 4.

(6√x + x) / 9

So, your simplified expression is (6√x + x) / 9.