Question

PLEASE HELP ASAP!!!!!!

Answer 1

`(1)/(axy)`

Explanation:

`(xy)/(a^2+a^3)` ×
`(a+a^2)/(x^2y^2)` ( factorise denominator and numerator of 2 fractions )

=
`(xy)/(a^2(1+a))` ×
`(a(1+a))/(x^2y^2)`

Cancel (1 + a) from both fractions

=
`(xy)/(a^2)` ×
`(a)/(x^2y^2)`

Cancel a and xy from both fractions

=
`(1)/(a)` ×
`(1)/(xy)`

=
`(1)/(axy)`

a ≠ 0 , x ≠ 0 , y ≠ 0

as this would would make the function undefined

Answer 2

Explanation:

`(xy)/(a^2+a^3)* (a+a^2)/(x^2y^2)`

Apply the fraction rule
`(a)/(b)* (c)/(d)=(a * c)/(b * d)` :

`\implies (xy(a+a^2))/(x^2y^2(a^2+a^3))`

Cancel the common factor
`xy` :

`\implies ((a+a^2))/(xy(a^2+a^3))`

Factor
`(a+a^2)=a(1+a) \ \ \textsf{and} \ \ a^2+a^3=a^2(1+a)` :

`\implies (a(1+a))/(xy \cdot a^2(1+a))`

Cancel the common factor
`a(1+a)` :

`\implies (1)/(axy)`

I think the "if" part is a, x and y cannot equal zero, as otherwise the expression will be undefined.

So I would put:
`x\\eq 0; y\\eq 0, a\\eq 0`