Question

Rationalize the denominator and simplily.​

Answer 1

Answer:

Step-by-step explanation:

(a-b)² = a²-2ab + b²

(a+b)(a-b)=a²-b²

$\frac{\sqrt{a+1} -2}{\sqrt{a+1}+2}= \frac{(\sqrt{a+1}-2)(\sqrt{a+1}-2 )}{(\sqrt{a+1}+2 )(\sqrt{a+1}-2)}$

             $=\frac{(\sqrt{a+1}-2 )^{2}}{(\sqrt{a+1} )^{2}-2^{2}}\\\\=\frac{(\sqrt{a+1})^ {2}-2*\sqrt{a+1}*2+2^{2} }{a+1-4}\\\\=\frac{a+1 - 4\sqrt{a+1}+4 }{a-3}\\\\=\frac{a+5-4\sqrt{a+1} }{a-3}$

Answer 2

Answer:

( (√ a+ 1) − 2 ) ^2/a-3

Step-by-step explanation: