Combining like terms?

[Dillinger4]

The problem is 5 - 1/3x6 + 3/x²-2x

I get all the way to 15x(x-2)(x-2) + x(x-2) + 9(x-2) / 3x(x-2)(x-2) but know i dont know what to do next. I know i can only cancel out common factors not terms. The numerator is still broken up into three terms so how do i combine like terms in the numerator?

[plenderj]

Is this the equation you typed out originally ?

5  -      1
     -----------
      3 . ( 6 +      3    )
                 --------
                 x^2 - 2x

[Acidic]

Dilenger you've gone wrong somewhere. I suppose your equations equals zero and you want to find X
in the first equation X cannot equal zero to get zero, but in the 2nd one can, could you please re-phrase the question and use brackets.

[Dillinger4]

Sorry. It's 5 - 1/3x - 6 + 3/x2-2x.

[Acidic]

do you mean
5 - (1/3x) - 6 + [3/(x^2-2x)] = 0 ?
in that case X is 2.3134703 according to my calc

[Dillinger4]

5 - 1 / (3x-6) + 3 / (x² - 2x)

[Acidic]

5 - 1 / (3x-6) + 3 / (x2 - 2x) =0
does not work for any value of X

think about it, as X tends to +0, the result tends to -infinity. As X tends to -0, the result tends towards +infinity. As X tends towards infinity (+ve or -ve) the result tends towards 5.

the closest it even gets to zero is:
-0.661705 when X is 1.029435

[Dillinger4]

Im not trying to find the value of x. It's just adding and subtracting rational expressions.

[Acidic]

to tidy it up? does it get tidier than that?

[Dillinger4]

5  -
          1
     -----------
      (3x -  6) 
                        + 
                   
                               3
                          -----------
                            x2 - 2x

[Acidic]

well I've got something, but I wouldn't be the least suprised if it's totally wrong:
5-[1/((3X-6)+3/(X^2-2X))]

As i think that if you have a fraction under a fraction you can bring the bottoms denominator to the very top:

= 5- (X^2-2X)/[(3X-3)-3]

= 5- (X(x-2)/[3+3(X-2)]

multiply everything be 3
= 15 - [X(X-2)]/[1+(X-2)]

then I get stuck

[Dillinger4]

5 - 1 / (3x - 6) + 3 / (x² - 2x)

5(3x-6)(x² - 2x) - (x² - 2x) + 3(3x-6) / (3x-6)(x² - 2x)

5(3x³ - 12x² + 12x) - x(x-2) + 9(x-2) / 3x(x-2)(x-2)

15x(x-2)(x-2) - x(x-2) + 9(x-2) / 3x(x-2)(x-2)

Now here is where im not sure what to do.

[NotLKH]

Assumption???
5 - 1 / (3x - 6) + 3 / (x² - 2x) = 0???

Start: 5 - 1 / (3x - 6) + 3 / (x2 - 2x)
Step 1: Multiply All terms by (3x-6)*(x²-2x)
::::: 5*(3x-6)*(x²-2x) - (1/(3x-6))*(3x-6)*(x²-2x) + 3*(1/(x²-2x))*(3x-6)*(x²-2x)

Step 2: Perform Multiplication on fractions:
:::::5*(3x-6)*(x²-2x) - (x²-2x) + 3*(3x-6)

Step 3: Result:
::::::15x³ - 61x²+71x-18 = 0

Now, let me check my math... oops!Bad Lou! -49 should be 71

So, Hows that!

[NotLKH]

Now, if you mean to get a single fraction, then I think it is:

(15x³ - 61x²+71x-18)/(3x³-12x²+12x)

[Dillinger4]

Lou. I come up with your answer for the numerator if i take this approach.

5(3x-6)(x² - 2x) - (x² - 2x) + 3(3x-6) / (3x-6)(x² - 2x)

5(3x³ - 12x² + 12x) - (x² - 2x) +(9x- 18) / 3x(x-2)(x-2)

15x³ - 60x² + 60x - x² + 2x + 9x -18

15x³ - 61x² + 71x - 18

The answer is supposed to be 15x² - 31x + 9 / 3x(x-2)

If i try to factor the resulting polynominal( 15x² - 31x + 9) to (? ?)(? ?) it dosent work for obvious reasons.

So i think i was on the right path with the last step i was at. 15x(x-2)(x-2) - x(x-2) + 9(x-2) / 3x(x-2)(x-2). Very confusing.