Question

PLEASE HELP ME AS QUICK AS POSSIBLE !!

Answer 1

1/(ab) if a ≠ 0, b ≠ 0, and (a+b) ≠ 0

Explanation:

You want the simplified form of 1/(a²+ab) +1/(ab+b²) and any applicable conditions.

Simplification

The expression is simplified by writing it over a common denominator and cancelling any common terms from numerator and denominator.

`(1)/(a^2+ab)+(1)/(ab+b^2)=(1)/(a^2+ab)\cdot(b)/(b)+(1)/(ab+b^2)\cdot(a)/(a)=(b+a)/(a^2b+ab^2)\\\\=(a+b)/(ab(a+b))=\boxed{(1)/(ab)\quad a\\e0,b\\e0,(a+b)\\e0}`

The given conditions ensure the denominator(s) will not be zero.