a=√8-√7 and a=1/b then fine a^2+b^2-3ab/a^2+ab+b^2
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Now a=√8-√7
a=1/b⇒ab=1
and b=1/a
=1/(√8-√7)
Rationalizing b:
⇒(1/(√8-√7))*(√8+√7)/(√8+√7)
⇒√8+√7/(8-7) ∵(a-b)x(a+b)=a²-b²
b=√8+√7
So a+b=2√8
a-b=-2√7 and
ab=1
Now numerator=a²+b²-3ab
=(a-b)²-ab
=(-2√7)²-1
=27
Now denominator=a²+b²+ab
=(a+b)²-ab
=(2√8)²-1
=31
∴ a²+b²-3ab/a²+ab+b²=27/31
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