(1÷1+√7)+(1÷√2+√3)+(2÷√3+√5) simplify
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This is a rationalisation problem,
Multiply the numerator and denominator by a value that makes the denominator vanish,

Thus we try to convert the denominator in the form
Multiply the numerator and denominator of the first part 1/(1 + √7) by (1-√7)
We get,
1-√7 / -6....(1)
Multiply the numerator and denominator of the second part 1/(√2 + √3) by (√2-√3)
We get,
-(√2-√3)...(2)
Multiply the numerator and denominator of the third part 2/(√3 + √5) by (√3 + √5)
We get,
-(√3 + √5)...(3)
Adding (1),(2) & (3),
√7-1/6 - √2 +√5
Multiply the numerator and denominator by a value that makes the denominator vanish,
Thus we try to convert the denominator in the form
Multiply the numerator and denominator of the first part 1/(1 + √7) by (1-√7)
We get,
1-√7 / -6....(1)
Multiply the numerator and denominator of the second part 1/(√2 + √3) by (√2-√3)
We get,
-(√2-√3)...(2)
Multiply the numerator and denominator of the third part 2/(√3 + √5) by (√3 + √5)
We get,
-(√3 + √5)...(3)
Adding (1),(2) & (3),
√7-1/6 - √2 +√5
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