Answer
$x = 5$
Work Step by Step
Factor all expressions to their simplest forms:
$\dfrac{5}{2(x - 1)} = \dfrac{15}{(x - 1)(x + 1)}$
The least common denominator, or LCD, incorporates all factors in the denominators of the fractions. In this case, the LCD is $2(x - 1)(x + 1)$.
Convert each fraction to an equivalent one by multiplying its numerator with whatever factor is missing between its denominator and the LCD:
$\dfrac{5(x + 1)}{2(x - 1)(x + 1)} = \dfrac{15(2)}{2(x - 1)(x + 1)}$
Multiply to simplify:
$\dfrac{5x + 5}{2(x - 1)(x + 1)} = \dfrac{30}{2(x - 1)(x + 1)}$
Multiply each side by the LCD to eliminate the fractions:
$5x + 5 = 30$
Subtract $5$ from each side of the equation:
$5x = 25$
Divide each side of the equation by $5$:
$x = 5$
