Answer
$x = 5$
Work Step by Step
Multiply each side of the equation by the least common denominator, or LCD, which is $x - 2$, in this case:
$\dfrac{4}{x - 2} \cdot (x - 2) = \dfrac{x - 1}{x - 2} \cdot(x- 2)$
Cancel out common terms in the numerators and denominators:
$4 = x - 1$
Add $1$ to each side of the equation:
$x = 5$
To check the solution, plug in $5$ for $x$ into the original equation:
$\dfrac{4}{5 - 2} = \dfrac{5 - 1}{5 - 2}$
Simplify the fractions:
$\dfrac{4}{3} = \dfrac{4}{3}$
Both sides are equal to one another; therefore, this solution is correct.
