Question

How do you simplify `(sqrta- sqrtb)/(sqrta+sqrtb)`?

Answer 1

Multiply both numerator and denominator by `sqrta - sqrtb`

`(sqrta - sqrtb)/(sqrta + sqrtb)= (sqrta - sqrtb)^2/(a - b)`

Answer 2

In this case, simplifying means rationalizing the denominator, that is getting rid of its square roots.

This can be done by using a well known algebraic identity: `x^2 - y^2 = (x+ y)(x - y)`.

In our case, we have to multiply the fraction by `(sqrt a - sqrt b)`:

`((sqrt a - sqrt b)(sqrt a - sqrt b)) / ((sqrt a - sqrt b)(sqrt a + sqrt b))` = `((sqrt a - sqrt b)^2) / ((sqrt a)^2 - (sqrt b)^2)` = `((sqrt a - sqrt b)^2) / (a -b)`