sqrt of u- sqrt of v over sqrt of u+sqrt of v

To simplify the expression (√u - √v) / (√u + √v), you can use a technique called rationalizing the denominator. Here's how you can do it step by step:

Step 1: Multiply both the numerator and denominator of the expression by the conjugate of the denominator. The conjugate of (√u + √v) is (√u - √v).

(√u - √v) / (√u + √v) * (√u - √v) / (√u - √v)

Step 2: Simplify the expression by using the distributive property and the difference of squares formula.

[ (√u)^2 - 2√u√v + (√v)^2 ] / [ (√u)^2 - (√v)^2 ]

Step 3: Simplify further by calculating the squares.

[ u - 2√uv + v ] / [ u - v ]

Therefore, the simplified expression of (√u - √v) / (√u + √v) is (u - 2√uv + v) / (u - v).