Rationalize the denominator and simplify. √(a+1)-2 / √(a+1)+2

Question

asked Jan 22, 2024 170k views

1 Answer

Stanislas Morbieu · Answer 1 · 2024-01-26T20:58:30+0000

Answer:

(a-4√(a+1)+5)/(a-3)

Explanation:

Given rational expression:

(√(a+1)-2)/(√(a+1)+2)

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is where we change the sign between the two terms of the binomial. So the conjugate of √(a+1)+2 is √(a+1)-2.

Therefore:

$\implies (√(a+1)-2)/(√(a+1)+2) \cdot (√(a+1)-2)/(√(a+1)-2)$

$\implies ((√(a+1)-2)(√(a+1)-2))/((√(a+1)+2)(√(a+1)-2))$

$\implies ((a+1)-4√(a+1)+4)/((a+1)-4)$

$\implies (a-4√(a+1)+5)/(a-3)$