How do you solve for x in 1/x + 3/(x-1) = 7/2?

Jun 12, 2018

$x = \frac{1}{7}$ or $x = 2$

Explanation:

$\frac{1}{x} + \frac{3}{x - 1} = \frac{7}{2}$

$\frac{\left(x - 1\right) + 3 x}{x \left(x - 1\right)} = \frac{7}{2}$

$\frac{4 x - 1}{x \left(x - 1\right)} = \frac{7}{2}$

$2 \left(4 x - 1\right) = 7 x \left(x - 1\right)$

$8 x - 2 = 7 {x}^{2} - 7 x$

$7 {x}^{2} - 15 x + 2 = 0$

$\left(7 x - 1\right) \left(x - 2\right) = 0$

$x = \frac{1}{7}$ or $x = 2$