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]
