Question

Rationalise the denominator and simplify

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Answer 1

Answer:

Step-by-step explanation:

Given\: \frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}Given

3

5

−2

6

2

6

−

5

=\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}\times \frac{3\sqrt{5}+2\sqrt{6}}{3\sqrt{5}+2\sqrt{6}}=

3

5

−2

6

2

6

−

5

×

3

5

+2

6

3

5

+2

6

=\frac{2\sqrt{6}(3\sqrt{5}+2\sqrt{6})-\sqrt{5}(3\sqrt{5}+2\sqrt{6})}{(3\sqrt{5})^{2}-(2\sqrt{6})^{2}}=

(3

5

)

2

−(2

6

)

2

2

6

(3

5

+2

6

)−

5

(3

5

+2

6

)

=\frac{6\sqrt{30}+24-15-2\sqrt{30}}{45-24}=

45−24

6

30

+24−15−2

30

=\frac{4\sqrt{30}+9}{21}=

21

4

30

+9

Therefore,

\frac{2\sqrt{6}-\sqrt{5}}{3\sqrt{5}-2\sqrt{6}}=\frac{4\sqrt{30}+9}{21}

3

5

−2

6

2

6

−

5

=

21

4

30

+9

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

hope this helps you buddy