Question

Just rationalize and simplify

Answer 1

$\mathsf{Given :\;\;\dfrac{\sqrt{a + 1} - 2}{\sqrt{a + 1} + 2}}$

$\mathsf{Multiplying\;Numerator\;and\;Denominator\;with\;\sqrt{a + 1} - 2,\;We\;get :}$

$\mathsf{\implies \dfrac{(\sqrt{a + 1} - 2)(\sqrt{a + 1} - 2)}{(\sqrt{a + 1} + 2)(\sqrt{a + 1} - 2)}}}$

$\mathsf{\implies \dfrac{(\sqrt{a + 1} - 2)^2}{(\sqrt{a + 1})^2 - (2)^2}}}$

$\mathsf{\implies \dfrac{(\sqrt{a + 1})^2 + (2)^2 - 2(\sqrt{a + 1})(2)}{a + 1 - 4}}}$

$\mathsf{\implies \dfrac{a + 1 + 4 - 4\sqrt{a + 1}}{a + 1 - 4}}}$

$\mathsf{\implies \dfrac{a + 5 - 4\sqrt{a + 1}}{a - 3}}}$

Answer 2

Answer:

(a+5)-4√(a+1) /(a-3)

Step-by-step 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)