Rational Expressions: -5x/(x^2 + 2x - 3) - 7/(x-1) + x/(x+3)

[Eligamer64]

Hello! I'm having trouble with rational equations and was wondering if you guys could help me. I recently bombed a test and really need to understand this so I can retake it... my summer is at stake!

Okay, so The first one I'm having trouble with is:

-5x/(x^2 + 2x - 3) - 7/(x-1) + x/(x+3)

And it asks you to, "Subtract, Multiply or Divide the rational expressions to the lowest possible terms."

I don't really know where to start or how to do it at all...

The next one is:

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

I started this one off by turning it into;

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

Then I crossed off the the (x+1)'s but my teacher said I got it wrong from there... Could someone explain how to do the rest of the problem?

Thanks so much!

(Plus, All of the expressions not in parenthesis like this; "x-1/x-1" Are one big division problem, One expression over another)
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Edited by stapel -- Reason for edit: formatting

 

[stapel]

I don't really know where to start or how to do it at all.

To learn "where to start or how to do it at all", try some online lessons. :wink:

 

[Denis]

-5x/(x^2 + 2x - 3) - 7/(x-1) + x/(x+3)

This may help you some...

1st, factor x^2 + 2x - 3 : (x - 1)(x + 3)
Now, let a = (x - 1) and b = (x + 3) ; rewrite the expression:

-5x / (ab) - 7 / a + x / b ; multiply by ab:
-5x - 7b + ax

Now substitute back in ; kapish?

Or you can "surprise" your teacher this way:
-5x - 7b + ax
ax - 5x - 7b
x(a - 5) - 7b

Answer:
x(a - 5) - 7b where a = x-1 and b=x+3 ; leave it like that :wink: