Subtractng Rational Expressions - Help

[mcruz65]

    x^2      -   2x     x    1
------------   -------     ------
3x^2 -5x -2     3x+1        x-2  

    x^2      -   2x     x    1
------------   -------     ------
(3x+1)(x-2)     3x+1        x-2

   x^2      -    2x(x-2)    x    1(3x+1)
------------   -----------     -----------
(3x+1)(x-2)    (3x+1)(x-2)     (3x+1)(x-2)

   x^2      -    2x^2 -4x    x    3x+1
------------   -----------     -----------
(3x+1)(x-2)    (3x+1)(x-2)     (3x+1)(x-2)

(-x^2 - 4x)(3x + 1)
--------------------
     (3x+1)(x-2)

(-x^2 - 4x)
------------
     x-2

x(-x - 4)
----------
   x - 2

Is this correct?

 

[mmm4444bot]

You did not follow the Order of Operations.

You need to multiply the two ratios first.

Then, subtract their product.

 

[Loren]

If your problem is...
\(\displaystyle \frac{x^2}{(3x+1)(x-2)}- \frac{2x}{3x+1}\cdot \frac{1}{x-2}\)

do the multiplication first. I ended up with \(\displaystyle \frac{x}{3x+1}\)

 

[mmm4444bot]

I just took a closer look at your work.

I have two more comments.

It looks like you were thinking that you need a common denominator before multiplying two fractions. This is not the case. We only need a common denominator to add or subtract fractions.

Also, you subtracted -4x and got -4x.

If we subtract -4x we get +4x.

PS: My final result agrees with Loren's