Question

Simplify:

$\frac{2}{\sqrt{7}+\sqrt{5}}+\frac{7}{\sqrt{12}-\sqrt{5}}-\frac{7}{\sqrt{12}-\sqrt{7}}$

• A. $5$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is D $0$

$\frac{2}{\sqrt{7}+\sqrt{5}}+\frac{7}{\sqrt{12}-\sqrt{5}}-\frac{7}{\sqrt{12}-\sqrt{7}}$

Rationalising the denominators, we have Given exp,
$\Rightarrow \frac{2}{(\sqrt{7}+\sqrt{5})}\times \frac{(\sqrt{7}-\sqrt{5})}{(\sqrt{7}-\sqrt{5})}+\frac{7}{(\sqrt{12}-\sqrt{5})}\times \frac{(\sqrt{12}+\sqrt{5})}{(\sqrt{12}+\sqrt{5})}-\frac{7}{(\sqrt{12}-\sqrt{7})}\times \frac{(\sqrt{12}+\sqrt{7})}{(\sqrt{12}+\sqrt{7})}$
$\Rightarrow \frac{2(\sqrt{7}-\sqrt{5})}{7-5}+\frac{7\sqrt{12}+\sqrt{5}}{12-5}-\frac{5\sqrt{12}+\sqrt{7}}{12-7}$

$\Rightarrow \frac{2(\sqrt{7}-\sqrt{5})}{2}+\frac{7\sqrt{12}+\sqrt{5}}{7}-\frac{5\sqrt{12}+\sqrt{7}}{5}$
$\Rightarrow \sqrt{7}-\sqrt{5}+\sqrt{12}+\sqrt{5}-\sqrt{12}-\sqrt{7}=0.$