SOLUTION: I need help with this equation, the last portion of the problem is neg. 14 over 2 squared minus 2x. I appreciate your help to solve the problem, I have a test tomorrow. 9/x

Algebra ->  Equations -> SOLUTION: I need help with this equation, the last portion of the problem is neg. 14 over 2 squared minus 2x. I appreciate your help to solve the problem, I have a test tomorrow. 9/x      Log On


   

Question 31724: I need help with this equation, the last portion of the problem is neg. 14 over 2 squared minus 2x. I appreciate your help to solve the problem, I have a test tomorrow.
9/x-2 + 7/x = -14/x2 – 2x
Answer by Cintchr(481) About Me  (Show Source):
You can put this solution on YOUR website!
+%289%2F%28x-2%29%29+%2B+%287%2Fx%29++=++%28-14%29%2F%28x%5E2-2x%29+
First, factor the denominator of the third fraction.
+%289%2F%28x-2%29%29+%2B+%287%2Fx%29++=++%28-14%29%2F%28x%28x-2%29%29+
Common Denominator is x(x-2)


Add the numerators
+%2816x-14%29%2F%28x%29%28x-2%29+=+%28-14%29%2F%28x%29%28x-2%29+
Multiply out the denominators
+%2816x-14%29%2F%28x%5E2-2x%29+=+%28-14%29%2F%28x%5E2-2x%29+
Cross Multiply
+%2816x-14%29%28x%5E2-2x%29+=+-14%28x%5E2-2x%29+
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%5E3+-14x%5E2+-4x+=+-14%28x%5E2-2x%29+
Distribute the -14 on the right side.
+16x%5E3-14x%5E2-4x+=+-14x%5E2%2B28x+
Move all parts to the left side
+16x%5E3-32x+=+0+
Factor out a 16x
+%2816x%29%28x%5E2-2%29=0+
Set all parts = to zero
+16x=0+ and +x%5E2-2+=0+
+x=0+ and +x%5E2+=+-2+
+x=0+ and +x=+sqrt%28-2%29+
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:
+%289%2F%28x-2%29%29+%2B+%287%2Fx%29++=++%28-14%29%2F%28x%5E2-2x%29+
First, factor the denominator of the third fraction.
+%289%2F%28x-2%29%29+%2B+%287%2Fx%29++=++%28-14%29%2F%28x%28x-2%29%29+
Common Denominator is x(x-2)

Now that the denominators are the same ... drop them.
+9%28x%29+%2B+7%28x-2%29++=++-14+
Distribute the 7 across the quantity
+9x+%2B+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