Answer:
Step-by-step explanation:
[tex]\dfrac{xy}{a^2+a^3}\times \dfrac{a+a^2}{x^2y^2}[/tex]
Apply the fraction rule [tex]\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a \times c}{b \times d}[/tex] :
[tex]\implies \dfrac{xy(a+a^2)}{x^2y^2(a^2+a^3)}[/tex]
Cancel the common factor [tex]xy[/tex] :
[tex]\implies \dfrac{(a+a^2)}{xy(a^2+a^3)}[/tex]
Factor [tex](a+a^2)=a(1+a) \ \ \textsf{and} \ \ a^2+a^3=a^2(1+a)[/tex] :
[tex]\implies \dfrac{a(1+a)}{xy \cdot a^2(1+a)}[/tex]
Cancel the common factor [tex]a(1+a)[/tex] :
[tex]\implies \dfrac{1}{axy}[/tex]
I think the "if" part is a, x and y cannot equal zero, as otherwise the expression will be undefined.
So I would put: [tex]x\neq 0; y\neq 0, a\neq 0[/tex]
