We are asked to simplify the given expression: $\frac{x}{x^2-4x}$.

AlgebraSimplificationRational ExpressionsFactorization
2025/6/6

1. Problem Description

We are asked to simplify the given expression: xx24x\frac{x}{x^2-4x}.

2. Solution Steps

First, we factor the denominator:
x24x=x(x4)x^2 - 4x = x(x-4).
Now we can rewrite the expression as:
xx(x4)\frac{x}{x(x-4)}.
Next, we can cancel the common factor xx in the numerator and the denominator, provided that x0x \neq 0.
xx(x4)=1x4\frac{x}{x(x-4)} = \frac{1}{x-4}.

3. Final Answer

The simplified expression is 1x4\frac{1}{x-4}.