Forget the name of it, but i need a review

1. Jun 11, 2009

austin1250

1. The problem statement, all variables and given/known data

I basiclly just need a little review and maybe some 1 to show me how to solve out the equation/and equation like it. here is an example:

2x+1 / x-1 + 1/ x+1 = ?

2. Relevant equations
?

3. The attempt at a solution
?

2. Jun 11, 2009

rock.freak667

I assume by ? you mean a number like 3 or 2 or even some function f(x)?

but here's a clue

$$\frac{1}{a} + \frac{1}{b}= \frac{a+b}{ab}$$

3. Jun 11, 2009

austin1250

by Question mark i mean it would equal like 2x + 1 / x^2 - 1 or something along those lines

4. Jun 11, 2009

rock.freak667

then just bring them to the same common denominator (x-1)(x+1). Do you know how to do that?

5. Jun 11, 2009

HallsofIvy

Staff Emeritus
I THINK you mean you want to add the two fractions (2x+1)/(x-1)+ 1/(x+1).

As Rock.freak667 said, you need to get "common denominators". Here, the common denominator is (x-1)(x+1). Multiply numerator and denominator of the first fraction by x+1 and numerator and denominator of the second fraction by x-1.

6. Jun 11, 2009

austin1250

no i forget, do you foil it ?

7. Jun 11, 2009

austin1250

yeah, ok I did that and i got

(2x^2-x-1)/(x2-2x+1) + (x+1)/ (x^2 -2x-2)

now what

8. Jun 11, 2009

rock.freak667

the denominator would be (x-1)(x+1)

now do as HallsofIvy said and

9. Jun 11, 2009

austin1250

that just confused me. i did what halls said and i got the answer you quoted. so i did it wrong?

10. Jun 11, 2009

rock.freak667

$$\frac{2x+1}{x-1} + \frac{1}{x-1}$$

$$= \frac{(2x+1)}{(x-1)(x+1)} + \frac{(x+1)}{(x-1)(x+1)}$$

since the denominators are both the same, you can just add the numerators now.

11. Jun 11, 2009

austin1250

did you copy that down wrong? its

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

12. Jun 11, 2009

rock.freak667

Sorry there, forgot to do some more typing, should be this

$$= \frac{(2x+1)(x+1)}{(x-1)(x+1)} + \frac{(x-1)}{(x-1)(x+1)}$$

13. Jun 11, 2009

HallsofIvy

Staff Emeritus
Now, austin1250, use "FOIL" to multiply (x-1)(x+1) carefully! It is NOT $x^2- 2x- 1$.

14. Jun 12, 2009

austin1250

oh did i say that? Sorry

x2-1