addition and substraction of rational expressions

Smith54

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Feb 20, 2009
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17
3x+1/x-1 - x-1/x-3 + x+1/x^2-4x+3
3x+1(x-3)/(x-1)(x-3) - (x-1)(x-1)/(x-3)(x-1)
3x^2-8x-3/(x-1)(x-3) - x^2-2x +2/(x-3)(x-1) + x+1/(x-3)(x-1)
2x^2-6x-5/(x-3(x-1) + (x+1)/(x-3)(x-1)
2x^2-5x-4/(x-3)(x-1) = 2(x-4)(x-1)/(x-3)(x-1) =

2(x-4)/(x-3)
 
Smith54 said:
(3x+1)/(x-1) - (x-1)/(x-3) + (x+1)/(x^2-4x+3)

[(3x+1)(x-3)]/[(x-1)(x-3)] - [(x-1)(x-1)]/[(x-3)(x-1)] + (x+1)/[(x-1)(x-3)] You forgot to type the third ratio, here!

(3x^2-8x-3)/[(x-1)(x-3)] - [x^2-2x +1]/[(x-3)(x-1)] + (x+1)/[(x-3)(x-1)] Note the arithmetic mistake that I corrected, in this line.

Typing rational expressions requires grouping symbols; if you leave them off, it's not clear what's in the numerator versus denominator.

Chances are that one day soon you'll be using mathematical software. You won't have the luxury of skipping the grouping symbols then, so you might as well get used to typing them now.

I see some other arithmetic mistakes, in the rest of your work, so throw it away, and continue from the point where I left off above.

You're doing fine, but watch out for those signs!

For example, if you subtract a grouped expression like (x^2 - 2x + 1), then each term is being subtracted:

-x^2 + 2x - 1

 
Different problem same subject.

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

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

y + 2(x-y) + (x^2 - xy) / x-y

3x-y-xy/x-y











)
 
Smith54 said:
x/x-y + 2 - x/y-x

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

y + 2(x-y) + (x^2 - xy) / x-y

3x-y-xy/x-y
Smitty, please start a NEW thread if posting a new problem.

You are NOT listening to what you were told:
your "x/x-y + 2 - x/y-x" should be x/(x-y) + 2 - x/(y-x) : brackets are IMPORTANT

Anyhow, your work in simplifying above is VERY wrong;
you definitely need classroom help.
 
Smith54 said:
1/1-x^2-1+x/1+x

Where are the grouping symbols above?

Without them, your typed expression means this:


\(\displaystyle \frac{1}{1} - x^2 - 1 + \frac{x}{1} + x\)


1/(-1)(1-x)(1+x) (1-x)(1+x)/-(1)(1-x)(1+x) +x((1+x)(1-x)/(1+x)(x-1)

I'm thinking that this line contains too many typographical errors to easily understand.
 
Smith54 said:
x/x-y + 2 - x/y-x

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

One of the symbols in red above is a typographical error, yes?

Please proofread your posts using the [Preview] button before submitting.





y + 2(x-y) + (x^2 - xy) / x-y

This typing means:

\(\displaystyle y + 2(x - y) + \frac{x^2 - xy}{x - y}\)




3x-y-xy/x-y

At one point, I thought the simplified ratio might be (3x - y)/(x - y), but with typographical errors and missing grouping symbols, I can't really say.

Please try again, and be more careful.
 
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