a-1+b-1÷a+b

Rewrite the expression using the negative exponent rule b-n=1bn.

1a+b-1÷a+b

Rewrite the division as a fraction.

1a+b-1a+b

Move b-1 to the denominator using the negative exponent rule b-n=1bn.

1a+1ab+b

1a+1ab+b

To write 1a as a fraction with a common denominator, multiply by bb.

1a⋅bb+1ab+b

Multiply 1a and bb.

bab+1ab+b

Combine the numerators over the common denominator.

b+1ab+b

To write b as a fraction with a common denominator, multiply by abab.

b+1ab+b⋅abab

Combine b and abab.

b+1ab+b(ab)ab

Combine the numerators over the common denominator.

b+1+b(ab)ab

Move b.

b+1+b⋅baab

Multiply b by b.

b+1+b2aab

b+1+b2aab

Simplify a^-1+(b^-1)÷a+b