Question 116066
{{{x/2}}} - {{{9/x}}} = {{{-7/2}}}
:
The common denominator would be 2x, right? If we multiply equation by 2x we can get rid of the denominators:
2x*{{{x/2}}} - 2x*{{{9/x}}} = 2x*{{{-7/2}}}
:
Cancel out the denominators and we have:
x(x) - 2(9) = x(-7)
:
x^2 - 18 = -7x
:
Arrange as a quadratic equation:
x^2 + 7x - 18 = 0
:
This factors to:
(x+9)(x-2) = 0
:
two solutions:
x = +2
and
x = -9
:
Check the x = -9 solution in the original equation:
{{{(-9)/2}}} - {{{9/(-9)}}} = {{{-7/2}}}
Using a common denominator, minus a minus is a plus
{{{-9/2}}} + {{{2/2}}} = {{{-7/2}}}
:
I'll let you check out the x=+2 solution