show that. a^-1/a^-1+b-1 + a^-1/a^-1 - b^-1 = 2b^2/b^2 - a^2
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To prove that a-1/a-1 +b-1 +a-1 /a-1-b-1 = 2b2 / b2-a2Lets take the LHS (Left Hand Side)
first:
=1/a-1/a+1/b + 1/a-1/a -1/b
Next take the LCM for the denominator, so it
becomes:
=1/a+b+a /ab + 1/a-b-a /ab
=1/axab /b+a+ 1/axab /b-a
Now 'a' gets cancelled in both the numerator and the denominator. So it becomes:
=1/axab /b+a+ 1/axab /b-a
=b/b+a+b /b-a
take the LCM of the denominator and so it
becomes:
=b(b-a)/(b+a)(b-a)+b(b+a)/(b-a)(b+a)
=b2 -ab /b2 -a2 +b2 +ab/b2 -a2
=b2 -ab +b2 +ab/b2 -a2
=b2+b2/b2-a2
=2b2/b2-a2 RHS (Right Hand Side)
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