simplify-x-2-x-1-1-2-x-1-1-2-x-2-

Question Number 9123 by j.masanja06@gmail.com last updated on 20/Nov/16

simplify

(x^{2} {(x + 1)}^{- 1 / 2} - {(x + 1)}^{1 / 2}) / x^{2}

Commented by tawakalitu last updated on 20/Nov/16

\frac{x^{2} {(x + 1)}^{- 1 / 2} - {(x + 1)}^{1 / 2}}{x^{2}}

= [x^{2} . \frac{1}{{(x + 1)}^{1 / 2}} - \frac{{(x + 1)}^{1 / 2}}{1}] \div x^{2}

= [\frac{x^{2}}{{(x + 1)}^{1 / 2}} - \frac{{(x + 1)}^{1 / 2}}{1}] \times \frac{1}{x^{2}}

Find the LCM in the braket .

= [\frac{x^{2} - (x + 1)}{{(x + 1)}^{1 / 2}}] \times \frac{1}{x^{2}}

= \frac{x^{2} - x - 1}{x^{2} \sqrt{x + 1}}