Question

rationalise 1/2-√3-1/√3+√2+5/3-√2​

Answer 1

Answer:

We rationalise term by term and then find the solution.

∴ 1/(√3 + √2)

= (√3 - √2)/{(√3 + √2) (√3 - √2)}

= (√3 - √2)/(3 - 2)

= (√3 - √2)/1

= √3 - √2,

2/(√5 - √3)

= 2 (√5 + √3)/{(√5 - √3) (√5 + √3)}

= 2 (√5 + √3)/(5 - 3)

= 2 (√5 + √3)/2

= √5 + √3 and

3/(√2 - √5)

= 3 (√2 + √5)/{(√2 - √5) (√2 + √5)}

= 3 (√2 + √5)/(2 - 5)

= 3 (√2 + √5)/(- 3)

= - √2 - √5.

∴ 1/(√3 + √2) - 2/(√5 - √3) - 3/(√2 - √5)

= (√3 - √2) - (√5 + √3) - (- √2 - √5)

= √3 - √2 - √5 - √3 + √2 + √5

= 0

This is the required rationalisation.