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Question
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
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Solution
`1/(sqrta + sqrtb) xx ((sqrta - sqrtb)/(sqrta - sqrtb)) = (sqrta - sqrtb)/(a - b)`
`{1/(sqrta + sqrtb) = (sqrta - sqrtb)/(a - b)}`
= `2/1 ((sqrt5 - sqrt3)/(5 - 3)) + ((sqrt3 - sqrt2)/(3-2)) - (3/1)((sqrt5 - sqrt2)/(5 - 2))`
= `cancel2 xx (sqrt5 - sqrt3)/cancel2 + (sqrt3 - sqrt2)/1 = cancel3 xx (sqrt5 - sqrt2)/cancel3`
= `cancelsqrt5 - cancelsqrt3 + cancelsqrt3 - cancelsqrt2 - cancelsqrt5 + cancelsqrt2`
= 0
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