# How do you simplify (4x-1)/(3x) + (x-8)/(5x)?

Oct 14, 2015

The answer is $\frac{23 x - 29}{15 x}$.

#### Explanation:

$\frac{4 x - 1}{3 x} + \frac{x - 8}{5 x}$

The LCD is $15$. Multiply each fraction so that its denominator will be $15 x$.

$\frac{4 x - 1}{3 x} \times \frac{5}{5} + \frac{x - 8}{5 x} \times \frac{3}{3} =$

(5(4x-1))/(5(3x))+(3(x-8))/(3(5x)=

Distribute the $5$ and the $3$ in the numerators and simplify $5 \cdot 3 x$ to $15 x$ and $3 \cdot 5 x$ to $15 x$.

$\frac{20 x - 5}{15 x} + \frac{3 x - 24}{15 x}$

Combine the numerators over the denominator $15 x$.

$\frac{20 x - 5 + 3 x - 24}{15 x}$

Combine like terms.

$\frac{20 x + 3 x - 5 - 24}{15 x} =$

$\frac{23 x - 29}{15 x}$