Rational Equation Help?

Question

Solve: 4/x^2-2x-3 = [-x/x-3] [-1/x+1]
I have:
Step 1: 4/(x+1) (x-3) = [-x/(x-3)] [-1/(x+1)]
Step 2: 4/(x+1) (x-3) ÷ (x+1) (x-3)
Step 3: [-x/(x-3)] [-1/(x+1)] ÷ (x+1) (x-3)
Step4: 4 = [-x (x+1)] - [1(x-3)]
Step 5: 4 = -x² - 1x – 1x + 3
Step 6: 4 = - x² - 2x + 3
Step 7: x² + 2x + 1 = 0
Ok where did I goof up?

Answer 1

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

(4/((x - 3)(x + 1))) = (x/((x - 3)(x + 1)))

as you can see

x = 4

Step 2 is where i believe you went wrong.

Lets do what you did

4/((x + 1)(x - 3)) = (-x/(x - 3))(-1/(x + 1))
4/((x + 1)(x - 3)) = (x/((x - 3)(x + 1))

now you would multiply both sides by (x + 1)(x - 3) and not divided. Once you have done that, you get (x + 1)(x - 3) will cancel out, which leaves you with 4 = x

Answer 2

You're making it way too complicated

4 / (x^2 - 2x - 3) = [-x / (x - 3)] [-1 / (x + 1)] {parentheses are really important in math - I assume this is your question}

factoring the denomenator of the left side of the equation leaves you with

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

which is the same as the denomenator of the right side of the equation, so.....

it looks like x = 4 just by sight


But, to answer your question: you should be multiplying, not dividing in steps 2 and 3. ----> that would give you the answer right away.

Keep in mind when you multiply a side by something you have to multiply the other side by the same thing in order to keep the equation equal. Otherwise it's just random and you made up your own equation!

Also, step 4 does not follow from step 3.
It looks like you're solving for x on the right side alone (cross-multiplying) and then setting that equal to what was left over of the left side?!?

The algebra is right in steps 5 through 7. Unfortunately, the mistake was before that.

Hope this helps.

Answer 3

Step 4 looks suspicious. Instead of a product on the right, you have a difference. The original eqn at the top appears to have a product on the right. Is it supposed to be a product, or a difference?

Also, you use the divide symbol when you're actually multiplying in steps 2 and 3.

Once I know the original problem is written correctly, I'll give you a solution if you like.

I think I see what you did in step 4. You tried to go from this:
[-x/(x-3)] [-1/(x+1)]
to this:
[-x (x+1)] - [1(x-3)].
However, you can't cross-multiply if the original problem was written correctly, because:
[-x/(x-3)] [-1/(x+1)] = x/((x-3)(x+1))
When you muliply that side by (x-3)(x+1), you get just x on that side. I trust you will know to apply this only if you typed the original problem correctly.

Answer 4

That's beyond me, can't remember that far back in high school!

This site might help you:

http://www.algebrahelp.com/calculators/equation/