Question

Just rationalize and simplify

Answer 1

(a+5)-4√(a+1) /(a-3)

Explanation:

√(a+1) - 2 / √(a+1) + 2

={√(a+1) - 2 }{√{(a+1) - 2 } / {√(a+1) + 2} {√(a+1) - 2 }

={√(a+1) - 2 }² / {√(a+1)}² - 2²

=[ {√(a+1)}² -4√(a+1) +4 ] / a+1-4

=[a+1-4√(a+1)+4] / (a-3)

=(a+5)-4√(a+1) /(a-3)

Answer 2

`\mathsf{Given :\;\;(√(a + 1) - 2)/(√(a + 1) + 2)}`

`\mathsf{Multiplying\;Numerator\;and\;Denominator\;with\;√(a + 1) - 2,\;We\;get :}`

`\mathsf{\implies ((√(a + 1) - 2)(√(a + 1) - 2))/((√(a + 1) + 2)(√(a + 1) - 2))}}`

`\mathsf{\implies ((√(a + 1) - 2)^2)/((√(a + 1))^2 - (2)^2)}}`

`\mathsf{\implies ((√(a + 1))^2 + (2)^2 - 2(√(a + 1))(2))/(a + 1 - 4)}}`

`\mathsf{\implies (a + 1 + 4 - 4√(a + 1))/(a + 1 - 4)}}`

`\mathsf{\implies (a + 5 - 4√(a + 1))/(a - 3)}}`