SOLUTION: Ok... the problem is (1/x)-(1/3)=(6/x^2). The instructions are to Solve the equation. I tried the problem and i got No Solution. I'm not really sure if this is the correct answer.

Algebra ->  Rational-functions -> SOLUTION: Ok... the problem is (1/x)-(1/3)=(6/x^2). The instructions are to Solve the equation. I tried the problem and i got No Solution. I'm not really sure if this is the correct answer.       Log On


   

Question 78424This question is from textbook Advanced Algebra
: Ok... the problem is (1/x)-(1/3)=(6/x^2). The instructions are to Solve the equation. I tried the problem and i got No Solution. I'm not really sure if this is the correct answer. I don't really understand this area in the chapter very much at all. Your help would be very Appreciated! Thanks! This question is from textbook Advanced Algebra

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx-1%2F3=6%2Fx%5E2

3x%5E2%281%2Fx-1%2F3%29=3x%5E2%286%2Fx%5E2%29 Multiply both sides by the LCD which is 3x%5E2

3x-x%5E2=18 Distribute

3x-x%5E2-18=0 Subtract 18 from both sides

-x%5E2%2B3x-18=0 Arrange in descending order
Now use the quadratic formula to solve for x:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B3x%2B-18+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%283%29%5E2-4%2A-1%2A-18=-63.

The discriminant -63 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -63 is + or - sqrt%28+63%29+=+7.93725393319377.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B3%2Ax%2B-18+%29



Since we have a complex answer, this means we have no real solution. So you were right and there are no solutions. If you graphed the 2 equations, you would notice that they never intersect.


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1/x)-(1/3)=(6/x^2)
The lcm is 3x^2.
Multiply thru by 3x^2 to get:
3x-x^2=18
x^2-3x+18=0
(x-6)(x+3)=0
x=6 or x=-3
---------
Checking these answers:
If x=6: 1/6-2/6=6/36------false
If x=-3: -1/3-1/3=6/9-----false
Therefore No Solution.
===========Cheers,
Stan H.