Question

Root 7-1 divided by root 7+1 - root 7+1 divide by root 7-1

Answer 1

Dear student
$$\begin{gathered} \frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}{\displaystyle +}{\displaystyle 1}}{\sqrt{7}{\displaystyle -}{\displaystyle 1}} \\ =\frac{{\displaystyle \sqrt{7}-1}}{{\displaystyle \sqrt{7}+1}}\times \frac{\sqrt{7}-1}{\sqrt{7}-1}-\frac{{\displaystyle \sqrt{7}+1}}{\sqrt{7}{\displaystyle -}{\displaystyle 1}}\times \frac{\sqrt{7}+1}{\sqrt{7}+1} \\ =\frac{{\left(\sqrt{7}-1\right)}^2}{{\left(\sqrt{7}\right)}^2-1^2}-\frac{{\left(\sqrt{7}+1\right)}^2}{{\left(\sqrt{7}\right)}^2-1^2} \\ =\frac{{\left(\sqrt{7}-1\right)}^2-{\left(\sqrt{7}+1\right)}^2}{7-1} \\ =\frac{\left(\sqrt{7}-1+\sqrt{7}+1\right)\left(\sqrt{7}-1-\sqrt{7}-1\right)}{6} \\ =\frac{2\sqrt{7}\times \left(-2\right)}{6} \\ =\frac{-2\sqrt{7}}{3} \end{gathered}$$
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