How do you solve 1/(2x) + 3/(x+7) = -1/x and find any extraneous solutions?

Jul 17, 2016

$x = - \frac{7}{3}$

Explanation:

First, you can write the equivalent equation:

$\frac{1}{2 x} + \frac{3}{x + 7} + \frac{1}{x} = 0$

and then have a single fraction, by multiplying all terms by 2x(x+7),

if $x \ne 0 \mathmr{and} x \ne - 7$:

1/cancel(2x)cancel(2x) (x+7)+3/cancel(x+7)2x(cancel(x+7))+1/cancelx2cancelx(x+7)=0

$x + 7 + 6 x + 2 x + 14 = 0$

$9 x + 21 = 0$

$x = - \frac{21}{9} = - \frac{7}{3}$