Question

a to the power minus 1 by a power minus 1 + b power minus 1 + a power minus 1 by a power minus 1 minus b power minus 1 is equal to minus 2 b square by a square minus b square​

Answer 1

hope you understand it .

Answer 2

Concept:

This is based on algebraic arithmetic and simple identities like

$(a-b)(a+b)=a^2-b^2$

Given:

[a^(-1)/(a^(-1)+b^(-1) )]+[a^(-1)/(a^(-1)-b^(-1) )]=(-2b^2)/(a^2-b^2 )

Find:

prove LHS and RHS are equal

Solution:

Solving LHS >

$(1/a)/(1/a+1/b)+(1/a)/(1/a-1/b)\\\\(1/a)/((a+b)/ab)+(1/a)/((b-a)/ab)\\\\ab/a(a+b) +ab/a(b-a) \\\\(b(b-a)+b(b+a))/(a^2-b^2 )\\\\b[b-a+b+a]/(a^2-b^2 )\\\\(2b^2)/(a^2-b^2 )$

RHS>

$(2b^2)/(a^2-b^2 )$

Hence, LHS is Equal to the RHS.