# How do you solve x-7+14/x=2 and check for extraneous solutions?

Dec 22, 2016

$\left\{7 , 2\right\}$ with $x \ne 0$

#### Explanation:

Put on a common denominator $\left(x\right)$.

$\frac{{x}^{2} - 7 x + 14}{x} = 2$

${x}^{2} - 7 x + 14 = 2 x$

${x}^{2} - 9 x + 14 = 0$

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

$x = 7 \mathmr{and} 2$

CHECK

7 - 7 + 14/7 =^? 2

0 + 2 = 2" "color(green)(√)

2 - 7 + 14/2 =^? 2

-5 + 7 = 2" "color(green)(√)

Hopefully this helps!