Question

9/(√5−√4) + 18/(√5+√4) − 9/(√5−√4)​

Answer 1

Answer:

$\frac{9}{ \sqrt{5} - \sqrt{4} } + \frac{18}{ \sqrt{5} - \sqrt{4} } - \frac{9}{ \sqrt{5} + \sqrt{4} } =18( \sqrt{5} + 4)$

Step-by-step explanation:

We can rationalise the terms given in the expression to do convert their denominators into integers. Also the formula to be used here is

$(\sqrt{a} + \sqrt{b} ) \times (\sqrt{a} - \sqrt{b} ) = a - b$

Rationalising

$\frac{9}{ \sqrt{5} - \sqrt{4} } \times \frac{ \sqrt{5} + \sqrt{4} }{ \sqrt{5} + \sqrt{4} } = 9( \sqrt{5} + \sqrt{4} )$

$\frac{18}{ \sqrt{5} + \sqrt{4} } \times \frac{ \sqrt{5} - \sqrt{4} }{ \sqrt{5} - \sqrt{4} } = 18( \sqrt{5 } - \sqrt{4} )$

therefore,

$\frac{9}{ \sqrt{5} - \sqrt{4} } + \frac{18}{ \sqrt{5} - \sqrt{4} } - \frac{9}{ \sqrt{5} + \sqrt{4} } = 9( \sqrt{5} + \sqrt{4} ) + 18( \sqrt{5} + \sqrt{4} ) - 9( \sqrt{5} - \sqrt{4} ) \\ = 18( \sqrt{5} + 4).$