How do you solve 3x+14/(5x)=31/5?

Mar 17, 2018

$x = \frac{2}{3} , \frac{7}{5}$

Explanation:

$\frac{15 {x}^{2}}{5 x} + \frac{14}{5 x} = \frac{31 x}{5 x} \rightarrow$ Find the least common denominator so that the fractions can be eliminated

$15 {x}^{2} + 14 = 31 x$

$15 {x}^{2} - 31 x + 14 = 0 \rightarrow$ Now multiply 15 and 14 together (it equals 210) and think of two numbers that add to -31 and multiply to 210

$15 {x}^{2} - 21 x - 10 x + 14 = 0$

$3 x \left(5 x - 7\right) - 2 \left(5 x - 7\right) = 0$

$\left(3 x - 2\right) \left(5 x - 7\right) = 0$

$3 x - 2 = 0$

$3 x = 2$

$x = \frac{2}{3}$

$5 x - 7 = 0$

$5 x = 7$

$x = \frac{7}{5}$