# How do you multiply 8/(x-4) -3=1/(x-10)?

Jul 10, 2018

$x = \frac{28}{3}$ or $x = 7$

#### Explanation:

we have to solve

$\frac{8}{x - 4} - 3 = \frac{1}{x - 10}$
simplifying the left-Hand side:

$\frac{8}{x - 4} - 3 = \frac{8 - 3 \left(x - 4\right)}{x - 4} = \frac{8 - 3 x + 12}{x - 4} = \frac{20 - 3 x}{x - 4}$
so we have

$\frac{20 - 3 x}{x - 4} = \frac{1}{x - 10}$
by cross multiplication we get

$\left(20 - 3 x\right) \left(x - 10\right) = x - 4$

multiplying out we get

$20 x - 3 {x}^{2} - 200 + 30 x = x - 4$

simplifying we have

$- 3 {x}^{2} + 49 x - 196 = 0$
dividing by $- 3$

${x}^{2} - \frac{49}{3} + \frac{196}{3} = 0$

${x}_{1 , 2} = \frac{49}{6} \pm \sqrt{{\left(\frac{49}{6}\right)}^{2} - \frac{196}{3}}$

note that

${\left(\frac{49}{6}\right)}^{2} - \frac{196}{3} = \frac{49}{36}$

so we get

${x}_{1} = \frac{28}{3}$

${x}_{2} = 7$