Question

prove that:(a+b)^-1(a^-1+b^-1)=1/ab​

Answer 1

Answer: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/a×ab /b+a+ 1/a×ab /b-a

Now 'a' gets cancelled in both the numerator and 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 -a2 +b2 +ab /b2 -a2

=b2 -ab +b2 +ab /b2 -a2

=b2+b2/b2-a2

=2b2/b2 -a2 ==== RHS (Right Hand Side)

Step-by-step explanation:

Answer 2

Thats Right

Step-by-step explanation:

(a+b)^-1 = 1/(a+b)

(a^-1+b^-1)= 1/a+1/b= (a+b)/ab

So The Multiplication Will Result

1 ( a+b)

------- × ------ == 1/ab

(a+b) ab