Question

Simplify
1/(sqrt(3) + sqrt(2)) = 2/(sqrt(5) - sqrt(3)) - 3/(sqrt(2) - sqrt(5))

Answer 1

Answer:

Step-by-step explanation:

Answer 2

We need to recall the following definition of conjugate.

Conjugate is a change in the sign in the middle of two terms.

($+$ to $-$ ) or ($-$ to $+$)

This problem is about the conjugation of a term.

Given:

$\frac{1}{(\sqrt{3}+\sqrt{2} ) } =\frac{2}{(\sqrt{5}-\sqrt{3} ) } -\frac{3}{(\sqrt{2}-\sqrt{5} ) }$

Multiply the numerator and denominator of each term by the conjugate of the denominator.

$\frac{1(\sqrt{3}-\sqrt{2} )}{(\sqrt{3}+\sqrt{2} )(\sqrt{3}-\sqrt{2} ) } =\frac{2(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3} ) (\sqrt{5}+\sqrt{3})} -\frac{3(\sqrt{2}+\sqrt{5} )}{(\sqrt{2}-\sqrt{5} ) (\sqrt{2}+\sqrt{5} )}$

$\frac{1(\sqrt{3}-\sqrt{2} )}{3-2} =\frac{2(\sqrt{5}+\sqrt{3})}{5-3} -\frac{3(\sqrt{2}+\sqrt{5} )}{2-5}$

$\frac{\sqrt{3}-\sqrt{2} }{1} =\frac{2(\sqrt{5}+\sqrt{3})}{2} -\frac{3(\sqrt{2}+\sqrt{5} )}{-3}$

$\sqrt{3}-\sqrt{2}=\sqrt{5}+\sqrt{3}+\sqrt{2}+\sqrt{5}$

$-\sqrt{2}=2\sqrt{5}+\sqrt{2}$

$2\sqrt{5}+2\sqrt{2}=0$

$2(\sqrt{5}+\sqrt{2})=0$