Sure! Let's solve this step-by-step.
1. Understand the given expression:
We have an expression:
[tex]\[
x^2 \cdot y \cdot \frac{x}{x^2} = y
\][/tex]
Let's simplify the left-hand side of the expression.
2. Simplify the expression:
[tex]\[
x^2 \cdot y \cdot \frac{x}{x^2}
\][/tex]
We can break down the fraction [tex]\(\frac{x}{x^2}\)[/tex]:
[tex]\[
\frac{x}{x^2} = \frac{1}{x}
\][/tex]
Now substitute this back into the original expression:
[tex]\[
x^2 \cdot y \cdot \frac{1}{x}
\][/tex]
Simplify further:
[tex]\[
x^2 \cdot \frac{1}{x} = x \Rightarrow x \cdot y = y
\][/tex]
3. Thin simplifies to:
[tex]\[
x \cdot y \cdot \frac{1}{x} = y
\][/tex]
This confirms our initial equality holds true in a more simple fashion.
4. Identify the target expression:
We need to find the value of the expression:
[tex]\[
x \cdot \frac{1}{x}
\][/tex]
5. Simplify the target expression:
The expression [tex]\(x \cdot \frac{1}{x}\)[/tex] can be simplified as:
[tex]\[
x \cdot \frac{1}{x} = 1
\][/tex]
Hence, the value of [tex]\(x \cdot \frac{1}{x}\)[/tex] is:
[tex]\[
1
\][/tex]
That is the final answer.
