square of u - square root of v/ square root of u + square root of v.
that makes no sense
It appears you want to rationalize the fraction. So, multiply top and bottom by
sqrt(u)-sqrt(v)
That gives you
(sqrt(u)-sqrt(v))^2/(u-v)
= (u - 2sqrt(uv) + v)/(u-v)
To simplify the expression (u^2 - √v) / (√u + √v), we need to rationalize the denominator. The rationalizing technique involves multiplying the numerator and denominator by the conjugate of the denominator.
The conjugate of the denominator, (√u + √v), is (√u - √v). So, we multiply the numerator and denominator by (√u - √v):
(u^2 - √v) * (√u - √v) / (√u + √v) * (√u - √v)
Now, let's simplify the expression:
Expanding the numerator:
(u^2 * √u) - (u^2 * √v) - (√v * √u) + (√v * √v)
Combining like terms:
u^2 * √u - u^2 * √v - √v * √u + √v^2
Simplifying:
u^2 * √u - u^2 * √v - √v * √u + v
Now, let's expand the denominator:
(√u * √u) - (√u * √v) + (√v * √u) - (√v * √v)
Simplifying:
u - √u * √v + √v * √u - v
Now, let's rewrite the entire expression:
(u^2 * √u - u^2 * √v - √v * √u + v) / (u - √u * √v + √v * √u - v)
And this is the simplified form of the expression (u^2 - √v) / (√u + √v).