Prove-that-h-1-1-h-1-h-1-1-please-

Question Number 54517 by hassentimol last updated on 05/Feb/19

Prove that

\frac{\sqrt{h + 1} - 1}{h} = \frac{1}{\sqrt{h + 1} + 1}

please \dots

Answered by Kunal12588 last updated on 05/Feb/19

l e t \sqrt{h + 1} = k

h + 1 = k^{2}

h = k^{2} - 1

\frac{\sqrt{h + 1} - 1}{h} = \frac{k - 1}{k^{2} - 1} = \frac{(k - 1)}{(k - 1) (k + 1)} = \frac{1}{k + 1} = \frac{1}{\sqrt{h + 1} + 1}

Commented by hassentimol last updated on 05/Feb/19

Thank you Sir

God bless you

Answered by math1967 last updated on 05/Feb/19

\frac{(\sqrt{h + 1} - 1) (\sqrt{h + 1} + 1)}{h (\sqrt{h + 1} + 1)} = \frac{h + 1 - 1}{h (\sqrt{h + 1} + 1)}

= \frac{1}{\sqrt{h + 1} + 1}

Commented by hassentimol last updated on 05/Feb/19

Thank you Sir