Question

Simplify this :
√x-1 - √x+1 / √x-1 + √x+1 ​

Answer 1

To simplify the given expression, multiply the numerator and denominator by the conjugate of the denominator. The simplified expression is -x+2√x-1.

Step-by-step explanation:

To simplify the given expression, we need to rationalize the denominator. We can do this by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √x-1 + √x+1 is √x-1 - √x+1.

So, multiplying the numerator and denominator by √x-1 - √x+1 gives:

(√x-1 - √x+1)(√x-1 - √x+1) / (√x-1 + √x+1)(√x-1 - √x+1)

Expanding and simplifying, we get:

(x-2√x+1) / (-1)

Which simplifies to:

-x+2√x-1