Rational Expressions - Trouble with Simplification of 2/(x^2+x-6) + 3/(x^3+2x^2-3x)

[markl77]

Hello!
There is this problem that I've done about 5 times and have come to the exact same stage every time, and I just can't figure it out.
So basically the initial problem looks like this : ( I don't know how to do the math text thingy).

2/(x^2+x-6) + 3/(x^3+2x^2-3x)
Which I simplify to :

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

From here when I make the denominators equal, I get to this :

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

Normally I would just factor this trinomial, but it's not possible. The answer I'm supposed to be left with (after multiplying it again) is 2x^2+x-4/x(x-1)(x+3)(x-2).

I'm just wondering how I simplified it incorrectly, and what I can do.
Thankyou!

 

[markl77]

Are you sure?
Substitute a value for x in the original expression,
then in the above...

yeah they both equal 5/28. I know I got the answer (simplifying) wrong, its just something that I'm missing with the simplification.

 

[ksdhart2]

Hello!
There is this problem that I've done about 5 times and have come to the exact same stage every time, and I just can't figure it out.
So basically the initial problem looks like this : ( I don't know how to do the math text thingy).

2/(x^2+x-6) + 3/(x^3+2x^2-3x)
Which I simplify to :

2/[(x-2)(x+3)] + 3/[x(x+3)(x-1)]

After adding in these missing grouping symbols (they are very important; make sure you understand why), I agree with your work up to this point.

From here when I make the denominators equal, I get to this :

[2x^2+3x-4]/[x(x-1)(x+3)(x-2)]

Again, I have inserted grouping symbols as needed. However, even with this correction, this step is not correct. Please share with us how you arrived at this conclusion.

Normally I would just factor this trinomial, but it's not possible. The answer I'm supposed to be left with (after multiplying it again) is [2x^2+x-4]/[x(x-1)(x+3)(x-2)]

Unfortunately, the answer as given to you is also incorrect. As Denis suggested, you can verify this by plugging in any value of x, say x = 5, and checking to see if you get the same result as the original equation, which you won't. The answer as given returns 17/160 when x = 5, but the original equation returns 49/480.

 

[mmm4444bot]

2/[(x-2)(x+3)] + 3/[x(x+3)(x-1)]

From here when I make the denominators equal, I get to this :

[2x^2+3x-4]/[x(x-1)(x+3)(x-2)]

These grouping symbols around denominators and numerators containing more than one factor or term are very important, to show the correct Order of Operations.

I'm just wondering how I simplified it incorrectly, and what I can do.

To see how you simplified it incorrectly, we need to see your steps going from the first line above to the second.

Also, what you can do is double-check your work. :cool:

 

[markl77]

After adding in these missing grouping symbols (they are very important; make sure you understand why), I agree with your work up to this point.



Again, I have inserted grouping symbols as needed. However, even with this correction, this step is not correct. Please share with us how you arrived at this conclusion.


QUOTE]
So, I have 2/[(x+3)(x-2)]+3/[x(x-1)(x+3)] I multiplied the numerator and denominator of the first fraction by x(x-1) and the numerator and denominator of the second fraction by (x-2) to make both of the denominators x(x-1)(x+3)(x-2). Then I joined the two fractions together because the denominators are now equal, and the two numerators are now 2x^2-2 and 3(x-2).
This has to be wrong because it obviously didn't work out, so I just need to know what the proper way to do it is.

 

[markl77]

Oh just kidding!
2x(x-1) cannot become 2(x^2-1), right? that's what I did to simplify it so I think that's why it is incorrect.

Yup, also I accidently put -4 as the constant for the answer in the back because I read the question below it by accident, it was supposed to be -6 so the textbook didn't get it wrong either.