Question

Simplify by rationalizing the denominator 1+√7/1-√7

Answer 1

[tex] \frac{1+\sqrt{7}}{1-\sqrt{7}} \\= \frac{1+\sqrt{7}}{1-\sqrt{7}} * \frac{1+\sqrt{7}}{1+\sqrt{7}} \\= \frac{(1+\sqrt{7})^2}{1^2-(\sqrt{7})^2} [/tex], here use formula (a-b)(a+b)=a^2-b^2
[tex]= \frac{1+2*\sqrt{7}+7}{1-7} \\= \frac{8+2*\sqrt{7}}{-6} \\= -\frac{4+\sqrt{7}}{3}[/tex]

Answer 2

1+√7/1-√7*1+√7/1+√7
(1+√7)(1+√7)/(1-√7)(1+√7)
1+2√7+7/(1-√7)^2
1+2√7+7/1-7
2√7+8/-6 =2(√7+4)/-6 =4+√7/-3