Simplify a^-1+(b^-1)÷a+b

Math
a-1+b-1÷a+b
Simplify each term.
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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
Multiply b by b by adding the exponents.
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Move b.
b+1+b⋅baab
Multiply b by b.
b+1+b2aab
b+1+b2aab
Simplify a^-1+(b^-1)÷a+b

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