Question

fast simplify this in pic​

Answer 1

Solution:-

⇒ $\frac{2}{\sqrt{5} + \sqrt{3}}$ $+ \frac{1}{\sqrt{3} + \sqrt{2}}$ $- \frac{3}{\sqrt{5} + \sqrt{2}}$

⇒ $\frac{2}{\sqrt{5} + \sqrt{3}}$ × $\frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}}$ $+ \frac{1}{\sqrt{3} + \sqrt{2}}$ × $\frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ $- \frac{3}{\sqrt{5} + \sqrt{2}}$ × $\frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}}$          [ By Rationalization ]

⇒ $\frac{2(\sqrt{5} - \sqrt{3})}{\sqrt{5}^{2} - \sqrt{2}^{2}}$ $+ \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3}^{2} - \sqrt{2}^{2}}$$- \frac{3(\sqrt{5} - \sqrt{2})}{\sqrt{5}^{2} - \sqrt{2}^{2}}$                [ By $(a + b) (a - b) = a^{2} - b^{2}$ ]

⇒ $\frac{2\sqrt{5} - 2\sqrt{3}}{5-3}$$+ \frac{\sqrt{3} - \sqrt{2}}{3-2}$$- \frac{3\sqrt{5} - 3\sqrt{2}}{5-2}$

⇒ $\frac{2\sqrt{5} - 2\sqrt{3}}{2}$$+ \frac{\sqrt{3} - \sqrt{2}}{1}$$- \frac{3\sqrt{5} - 3\sqrt{2}}{3}$

⇒ $\frac{6\sqrt{5} - 6\sqrt{3} + 6\sqrt{3} - 6\sqrt{2} - 6\sqrt{5} - 6\sqrt{2}}{6}$

⇒ $\frac{0}{6}$

⇒ 0

∴ The simplification of the $\frac{2}{\sqrt{5} + \sqrt{3}}$ $+ \frac{1}{\sqrt{3} + \sqrt{2}}$ $- \frac{3}{\sqrt{5} + \sqrt{2}}$ = 0.

Some important terms:-

Rationalization is the process of eliminating a radicals or imaginary number from the denominator of an algebraic fraction.

For Example:- $\frac{1}{\sqrt{3}} + \frac{1}{\sqrt{2} - \sqrt{5}}$  

                   ⇒ $\frac{1}{\sqrt{3}}$ × $\frac{\sqrt{3}}{\sqrt{3}}$ $+ \frac{1}{\sqrt{2} - \sqrt{5}}$ × $\frac{\sqrt{2} + \sqrt{5}}{\sqrt{2} + \sqrt{5}}$     [ Change the sign after multiplying it by the numerator and denominator ]

                   ⇒ $\frac{\sqrt{3}}{3}$ $+ \frac{\sqrt{2} + \sqrt{5}}{\sqrt{2}^{2} - \sqrt{5}^{2}}$

                   ⇒ $\frac{\sqrt{3}}{3}$ $+ \frac{\sqrt{2} + \sqrt{5}}{2-5}$

                   ⇒ $\frac{\sqrt{3}}{3}$ $+ \frac{\sqrt{2} + \sqrt{5}}{-3}$

                   ⇒ $\frac{{\sqrt{3} + \sqrt{2} + \sqrt{5}}}{-3}$

                   ⇒ $\frac{{\sqrt{3} + \sqrt{2} - \sqrt{5}}}{3}$

Answer 2

Answer:

sorry bro or sis aap hamari vajah se distrub hue

btw good afternoon