Answer
$a = 4$
To check the solution, plug in $4$ for $a$ into the original equation:
$\frac{4}{2(4)} = \frac{5}{4 + 6}$
Simplify:
$\frac{4}{8} = \frac{5}{10}$
Simplify the fractions:
$\frac{1}{2} = \frac{1}{2}$
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 two fractions. The least common denominator, or LCD, is $2a(a + 6)$, 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:
$\frac{4(a + 6)}{2a(a + 6)} = \frac{5(2a)}{2a(a + 6)}$
Distribute and multiply to simplify:
$\frac{4a + 24}{2a(a + 6)} = \frac{10a}{2a(a + 6)}$
Multiply both sides of the equation by $2a(a + 6)$ to eliminate the fractions:
$4a + 24 = 10a$
Subtract $4a$ from each side of the equation:
$24 = 6a$
Divide both sides of the equation by $6$:
$a = 4$
To check the solution, plug in $4$ for $a$ into the original equation:
$\frac{4}{2(4)} = \frac{5}{4 + 6}$
Simplify:
$\frac{4}{8} = \frac{5}{10}$
Simplify the fractions:
$\frac{1}{2} = \frac{1}{2}$
Both sides are equal to one another; therefore, this solution is correct.