## Precalculus (6th Edition) Blitzer

$\displaystyle \frac{8x+1}{4x-1}, \quad x\neq 0, \displaystyle \frac{1}{4}$
Complex rational expressions have rational expressions in the numerator or/and in the denominator. Here, both the numerator and the denominator contain $\displaystyle \frac{1}{x}$ ( 0 is excluded from the domain). Multiplying each with x would get rid of the fractions. $\displaystyle \frac{x}{x}\times\frac{8+\frac{1}{x}}{4-\frac{1}{x}}=\frac{8x+1}{4x-1}, \quad x\neq 0, \displaystyle \frac{1}{4}$