Question

please help me with this ques

Answer 1

To prove that a^-1/a^-1+b^-1+a^-1/a^-1-b^-1= 2b2/b^2-a^2
Lets 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/a×ab /b+a+ 1/a×ab /b-a
Now 'a' gets cancelled in both the numeratorand the denominator. So it becomes:=
1/a×ab /b+a+ 1/a×ab /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-=a^2+b^2+ab /b^2-a^2
=b2-ab+b2+ab/b2-a2
=b2+b2/b^2-a^2
=2b^2/b^2-a^2==== RHS (Right Hand Side)
I hope this answer was helpful. . .

Answer 2

LHS= 1/a/(1/a+1/b) +1/a(1/a-1/b)=1/a/(a+b/ab)+1/a/(b-a)/ab =1/a*ab/(a+b)+1/a*ab(b-a)=b/(a+b)+b/(b-a)=b^2-ab+ab+b^2/(b^2-a^2)=2b^2/(b^2-a^2)=RHS