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.
4X^0.5/(6-X^0.5) =
4X^0.5(6+X^0.5)/(6-X^0.5)(6+X^0.5) =
(24x^0.5 + 4x)/(36-X) =
(24sqrt(X)+4x)/(36-X).
Recall: (a+b)(a-b) = a^2-b^2.
sqrt X = X^0.5.
To simplify the expression (4√x)/(6-√x), you are correct that you can further simplify it.
Here's how to proceed:
Step 1: Rationalize the denominator.
To get rid of the radical in the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (6+√x).
By multiplying the numerator and denominator by (6+√x), we have:
(4√x) * (6+√x) / [(6-√x) * (6+√x)]
Step 2: Simplify the expression.
In the numerator, we have:
(4√x) * (6+√x) = 24√x + 4x
In the denominator, we have:
(6-√x) * (6+√x) = 36 - x
So the simplified expression becomes:
(24√x + 4x) / (36 - x)
Step 3: Factor out common terms, if possible.
In this case, there are no common factors that can be factored out from both the numerator and denominator. Therefore, the expression is already in its simplest form:
(24√x + 4x) / (36 - x)
And that's it! The expression (4√x)/(6-√x) simplifies to (24√x + 4x) / (36 - x).