Chapter 7 - Algebraic Fractions - 7.5 - Fractional Equations and Problem Solving - Problem Set 7.5 - Page 306: 27

$n = 37$

1. Multiply by $49-n$ on both sides of the equation to remove the fractions: $\frac{n}{49-n} = 3 + \frac{1}{49-n}$ $n = 3(49-n) + \frac{1(49-n)}{49-n}$ $n = 3(49-n) + \frac{49-n}{49-n}$ 2. Simplify the fraction $n = 147 - 3n + 1$ $-147 + n + 3n - 1 = 0$ $-148 + 4n = 0$ $4(-37 + n) = 0$ (Factor $4$ out) $-37 + n = 0$ $n = 37$