Question

simplify with full explanation​

Answer 1

Step-by-step explanation:

This is solution of your question.

Answer 2

Answer:

answer. 1

Step-by-step explanation:

$\frac{1}{ \sqrt{4} + \sqrt{5} } + \frac{1}{ \sqrt{5} + \sqrt{6} } + \frac{1}{ \sqrt{6} + \sqrt{7} } + \frac{ 1 }{\sqrt{7} + \sqrt{8}} + \frac{ 1 }{\sqrt{8} + \sqrt{9}} \\ \\ \frac{1}{ \sqrt{5} + \sqrt{4} } = \frac{1}{ \sqrt{5} + \sqrt{4} } \times \frac{ \sqrt{5} - \sqrt{4} }{ \sqrt{5} - \sqrt{4} } = \sqrt{5} - \sqrt{4} \\ \\ \\ \frac{1}{ \sqrt{6} + \sqrt{5} } = \sqrt{6} - \sqrt{5} \\ \\ \\ \\ \\ \frac{1}{ \sqrt{7} + \sqrt{6} } = \sqrt{8} - \sqrt{7} \\ \\ \\ \\ \\ \frac{1}{ \sqrt{8} + \sqrt{7} } = \sqrt{8} - \sqrt{7} \\ \\ \\ \\ \frac{1}{ \sqrt{9} + \sqrt{8} } = \sqrt{9} - \sqrt{8} \\ \\ \\ \\ \frac{1}{ \sqrt{4} + \sqrt{5} } + \frac{1}{ \sqrt{5} + \sqrt{6} } + \frac{1}{ \sqrt{6} + \sqrt{7} } + \frac{ 1 }{\sqrt{7} + \sqrt{8}} + \frac{ 1 }{\sqrt{8} + \sqrt{9}} = \\ \\ = \sqrt{5} - \sqrt{4} + \sqrt{6} - \sqrt{5} + \sqrt{7} - \sqrt{6} + \sqrt{8} - \sqrt{7} + \sqrt{9} - \sqrt{8} \\ \\ = \sqrt{9} - \sqrt{4} \\ \\ = 3 - 2 \\ \\ = 1$