Question

$\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}=\frac{a}{b}\text{find}a+b=?$

Answer 1

$\frac{\sqrt{80}-\sqrt{112}}{\sqrt{45}-\sqrt{63}}=\frac{4\sqrt{5}-4\sqrt{7}}{3\sqrt{5}-3\sqrt{7}}\times \frac{3\sqrt{5}+3\sqrt{7}}{3\sqrt{5}+3\sqrt{7}}$

$=\frac{60+12\sqrt{35}-12\sqrt{35}-84}{45-63}$

$=\frac{-24}{-18}=\frac{4}{3}$