simplify: (2±√x)/(2-√x)

I would rationalize, but multiplying numerator and denominator by (2+sqrtx)

12x+20y+15z=-60

To simplify the expression (2 ± √x) / (2 - √x), we will follow these steps:

Step 1: Multiply the numerator and the denominator by the conjugate of the denominator. In this case, the conjugate of (2 - √x) is (2 + √x).

So, we have:
((2 ± √x) / (2 - √x)) * ((2 + √x) / (2 + √x))

Step 2: Apply the distributive property to simplify the expression.

The numerator becomes: (2 ± √x) * (2 + √x)
The denominator becomes: (2 - √x) * (2 + √x)

Step 3: Simplify both the numerator and the denominator.

Numerator:
We can use the distributive property to simplify the numerator.
(2 ± √x) * (2 + √x) = 2(2) + 2(√x) ± (√x)(2) ± (√x)(√x)
= 4 + 2√x ± 2√x ± x
= 4 ± x

Denominator:
Similarly, we can use the distributive property to simplify the denominator.
(2 - √x) * (2 + √x) = 2(2) + 2(√x) - (√x)(2) - (√x)(√x)
= 4 + 2√x - 2√x - x
= 4 - x

Step 4: Write the simplified expression.

Putting it all together, we have:
((2 ± √x) / (2 - √x)) * ((2 + √x) / (2 + √x)) = (4 ± x) / (4 - x)

So, the simplified expression is (4 ± x) / (4 - x).