Answer
$b = -5$
To check the solution, plug in $-5$ for $b$ into the original equation:
$\frac{3}{-5 + 2} = \frac{6}{-5 - 1}$
Simplify the fractions:
$\frac{3}{-3} = \frac{6}{-6}$
Reduce fractions:
$-1 = -1$
Both sides are equal to one another; therefore, this solution is correct.
Work Step by Step
Before we can solve the equation, find the least common denominator for the three fractions. The least common denominator, or LCD, is $(b + 2)(b - 1)$, in this case. Convert each fraction to an equivalent one by multiplying its numerator with whatever factor is missing between its denominator and the LCD:
$\frac{3(b - 1)}{(b + 2)(b - 1)} = \frac{6(b + 2)}{(b + 2)(b - 1)}$
Distribute:
$\frac{3b - 3}{(b + 2)(b - 1)} = \frac{6b + 12}{(b + 2)(b - 1)}$
The fractions on both sides of the equation have the same denominator, so we can multiply each side of the equation by $(b + 2)(b - 1)$ to eliminate the fractions:
$3b - 3 = 6b + 12$
Subtract $6b$ from each side of the equation:
$-3b - 3 = 12$
Add $3$ to each side of the equation:
$-3b = 15$
Divide each side of the equation by $-3$:
$b = -5$
To check the solution, plug in $-5$ for $b$ into the original equation:
$\frac{3}{-5 + 2} = \frac{6}{-5 - 1}$
Simplify the fractions:
$\frac{3}{-3} = \frac{6}{-6}$
Reduce fractions:
$-1 = -1$
Both sides are equal to one another; therefore, this solution is correct.
