Answer :

Let's start solving the expression [tex]\(\frac{x^2 y^3 + x y^2}{x y}\)[/tex] step by step.

1. Expression: [tex]\(\frac{x^2 y^3 + x y^2}{x y}\)[/tex]

2. Factor out common terms from the numerator:

We notice that each term in the numerator has a factor of [tex]\(xy\)[/tex]. Let's factor [tex]\(xy\)[/tex] out from the numerator:
[tex]\[ x^2 y^3 + x y^2 = x y \cdot (x y^2) + x y \cdot y = x y (x y^2 + y) \][/tex]

3. Rewrite the expression using the factored form:
[tex]\[ \frac{x y (x y^2 + y)}{x y} \][/tex]

4. Simplify the fraction:

We see that [tex]\(xy\)[/tex] in the numerator and the denominator can cancel each other out:
[tex]\[ \frac{x y (x y^2 + y)}{x y} = x y^2 + y \][/tex]

Therefore, when simplified, the expression [tex]\(\frac{x^2 y^3 + x y^2}{x y}\)[/tex] is equal to [tex]\(y (x y + 1)\)[/tex].

Thus, the simplified form of the expression [tex]\(\frac{x^2 y^3 + x y^2}{x y}\)[/tex] is:
[tex]\[ y (x y + 1) \][/tex]