deverhardt 3 years ago Solve the equation for x. -1+((2x)/(x+3))=((-2)/(x+2))

1. deverhardt

Multiply the equation by the LCD.

2. deverhardt

Sorry I should have stated to solve the equation for x.

3. estudier

K, let's start again.....

4. deverhardt

okay

5. estudier

What is it u want to do?

6. deverhardt

|dw:1350674953315:dw|

7. estudier

Yes, so what is it u want to do?

8. deverhardt

Multiply (-1), (2x/x+3), and (-2x/x+2) by the LCD of (x+3) and (x+2).

9. estudier

OK, that is the long way around of solving for x. You will get to the same place at the end. I guess your teacher has told u to do it that way, right?

10. deverhardt

yes

11. estudier

LCD of (x+3) and (x+2) is just (x+3)(x+2) I will leave you to it, it is not too hard to do.

12. deverhardt

Okay. Thank you. I know the answer is (-1,0). I just wanted to make sure I was on the right path.

13. estudier

U should also note that x=-3 and x = -2 are not defined for this equation.

14. deverhardt

correct

15. deverhardt

Could you please explain the shorter way of doing this type of equation.

16. estudier

If you add the terms on the left side -> (x-3)/(x+3) = -2/(x+2) Cross multiply -> (x-3)(x+2) = -2(x+3) -> x^2 -x -6 = -2x - 6 -> x^2 + x = 0 -> x( x +1) = 0 -> x = 0 or -1

17. deverhardt

Wow that is much quicker! Thank you so much

18. estudier

yw:)

19. estudier

The other way reminds you that the original equation is not defined for x=-3 and x = -2 But with some practice you will not need reminding....

20. deverhardt

Could I use this shorter way for this equation as well? (see drawing)

21. deverhardt

|dw:1350677688912:dw|

22. estudier

Yes, u can.

23. deverhardt

Thanks. When I add the terms on the LHS I get (z+1) / (z-6). Is this correct?

24. estudier

No, (z+1) + 1*(z-6) / (z-6) = (2z-5) / (z-6)

25. deverhardt

Gotcha. Thanks