Question

solve for x.
\\(\frac{3}{x^2 - x} = \frac{1}{x - 1}\\)
if there are two solutions, write one solution in each box. if there is one solution, leave the second box empty.
\\(x = \square\\) or \\(x = \square\\)

Explanation:

Step1: Factor the denominator

Factor \(x^2 - x\) as \(x(x - 1)\), so the equation becomes \(\frac{3}{x(x - 1)}=\frac{1}{x - 1}\).

Step2: Multiply both sides by \(x(x - 1)\) (note \(x

eq0\) and \(x
eq1\) to avoid division by zero)
\(3 = x\).

Step3: Check the solution

Substitute \(x = 3\) into the original equation: left side \(\frac{3}{3^2 - 3}=\frac{3}{6}=\frac{1}{2}\), right side \(\frac{1}{3 - 1}=\frac{1}{2}\). It works. Also, we need to check the excluded values \(x = 0\) and \(x = 1\): for \(x = 0\), denominator \(x^2 - x = 0\), undefined; for \(x = 1\), denominator \(x - 1 = 0\), undefined. So only \(x = 3\) is valid.

Answer:

\(x = \boldsymbol{3}\) or \(x = \boldsymbol{}\)