Question

simplify each of the following by rationalising the denominator
1)√ 7 - √ 5/
√7+ √5
​

Answer 1

Answer:

6-√35

Step-by-step explanation:

$\frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} + \sqrt{5} } \times \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} - \sqrt{5} } = \frac{( \sqrt{7} - \sqrt{5} )^{2} }{( \sqrt{7} ) {}^{2} {} - ( \sqrt{5}) ^{2} }$

$= \frac{7 + 5 - 2 \sqrt{35} }{7 - 5}$

$\frac{12 - 2 \sqrt{35} }{2}$

${6 - \sqrt{35} }$