Question 31724
{{{ (9/(x-2)) + (7/x)  =  (-14)/(x^2-2x) }}}
First, factor the denominator of the third fraction.
{{{ (9/(x-2)) + (7/x)  =  (-14)/(x(x-2)) }}}
Common Denominator is x(x-2)
{{{ (9(x)/(x-2)(x)) + (7(x-2)/x(x-2))  =  (-14)/(x(x-2)) }}}
{{{ (9x/(x)(x-2)) + ((7x-14)/x(x-2))  =  (-14)/(x(x-2)) }}}
Add the numerators
{{{ (16x-14)/(x)(x-2) = (-14)/(x)(x-2) }}}
Multiply out the denominators
{{{ (16x-14)/(x^2-2x) = (-14)/(x^2-2x) }}}
Cross Multiply
{{{ (16x-14)(x^2-2x) = -14(x^2-2x) }}}
FOIL the left side
F: 16x * x^2 = 16x^3
O: 16x * -2x = -32x
I: -14 * x^2 = -14x^2
L: -14 * -2x = 28x
Bring them together
{{{ 16x^3 -14x^2 -4x = -14(x^2-2x) }}}
Distribute the -14 on the right side.
{{{ 16x^3-14x^2-4x = -14x^2+28x }}}
Move all parts to the left side
{{{ 16x^3-32x = 0 }}}
Factor out a 16x
{{{ (16x)(x^2-2)=0 }}}
Set all parts = to zero
{{{ 16x=0 }}} and {{{ x^2-2 =0 }}}
{{{ x=0 }}} and {{{ x^2 = -2 }}}
{{{ x=0 }}} and {{{ x= sqrt(-2) }}}
since no denominator can be equal to zero, and 99.99999 times out of 100 we HATE negative roots, this problem has NO solutions.






I tried this a second way ... and sitll came up with x = 0
This is what I had:
{{{ (9/(x-2)) + (7/x)  =  (-14)/(x^2-2x) }}}
First, factor the denominator of the third fraction.
{{{ (9/(x-2)) + (7/x)  =  (-14)/(x(x-2)) }}}
Common Denominator is x(x-2)
{{{ (9(x)/(x-2)(x)) + (7(x-2)/x(x-2))  =  (-14)/(x(x-2)) }}}
Now that the denominators are the same ... drop them.
{{{ 9(x) + 7(x-2)  =  -14 }}}
Distribute the 7 across the quantity
{{{ 9x + 7x-14  =  -14 }}}
Combine x terms
{{{ 16x-14  =  -14 }}}
add 14 to both sides
{{{ 16x = 0 }}}
Divide by 16
{{{ x=0 }}}
The problem with this is that 0 makes the denominator on the second fraction equal to 0, and division by 0 is undefined.  
So for this problem, there is no soulution.
When graphed, it does not cross the x-axis