Question

simlify: 1/2-root3 - 1/root3+root2 + 5/3-root2​

Answer 1

Step-by-step explanation:

−

3

+

2

1

+

3−

2

5

now we factorise each expression one by one

\frac{1}{2 - \sqrt{3} } = 2 + \sqrt{3}

2−

3

1

=2+

3

\frac{5}{3 - \sqrt{2} } = \frac{5(3 + \sqrt{2}) }{9 - 2} = \frac{15 + 5 \sqrt{2} }{7}

3−

2

5

=

9−2

5(3+

2

)

=

7

15+5

2

\frac{1}{ \sqrt{3} + \sqrt{2} } = \sqrt{3} - \sqrt{2}

3

+

2

1

=

3

−

2

now simplification

2 + \sqrt{3} [/tex]-(\sqrt{3} - \sqrt{2} [/tex])+\frac{15 + 5 \sqrt{2} }{7} [/tex]

=\frac{15 + 5 \sqrt{2}+14+7\sqrt{2} }{7} [/tex]=\frac{29 + 12 \sqrt{2} }{7} [/tex]

hope it helped you