Question

simplify the rational expression.
\\(\frac{30x}{20x^2 - 5x}\\)
first, list any restricted value(s).

Explanation:

Step1: Find restricted values

To find restricted values, set the denominator equal to zero: $20x^2 - 5x = 0$. Factor out $5x$: $5x(4x - 1) = 0$.

Step2: Solve for x

Set each factor equal to zero: $5x = 0$ gives $x = 0$; $4x - 1 = 0$ gives $x = \frac{1}{4}$.

Step3: Simplify the expression

Factor numerator and denominator: Numerator is $30x = 5x \cdot 6$; Denominator is $20x^2 - 5x = 5x(4x - 1)$. Cancel common factor $5x$ (note $x
eq 0$): $\frac{30x}{20x^2 - 5x} = \frac{6}{4x - 1}$.

Answer:

Restricted values: $x = 0$ and $x = \frac{1}{4}$; Simplified expression: $\frac{6}{4x - 1}$