Question

Find the value of      1                1
                         ______  +    ______
                         1 + √2         √2 + √3

URGENT!!!!

Answer 1

1/(1+√2)+1/(√2+√3)
=1/(√2+1)+1/(√3+√2)
=1*(√2-1)/(√2+1)*(√2-1)+1*(√3-√2)/(√3+√2)*(√3-√2)
=(√2-1)/(2-1)+(√3-√2)/(3-2)
=√2-1+√3-√2
=√3-1

Answer 2

[tex] \frac{1}{ 1+\sqrt{2} } + \frac {1}{\sqrt{2} + \sqrt{3} } \\ \\ [/tex]

Multiply the first fraction in the numerator and denominator by √2-1. The second fraction, multiply and divide by √3 - √2.

[tex] \frac{ ( \sqrt{2} -1) }{ (\sqrt{2}+1)(\sqrt{2}-1) } + \frac{ (\sqrt{3} - \sqrt{2)}}{ (\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2) } } \\ [/tex]

Now