## anonymous one year ago I cant seem to figure this out help please :) What is the simplified form of 2 over x squared plus x minus 1 over x ?

1. anonymous

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

2. anonymous

@mathstudent55 @MTALHAHASSAN2 @markaskingalexandria1 @animalfan1 @abs202 @Summersnow8 @RedNeckOutLaw

3. MTALHAHASSAN2

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4. MTALHAHASSAN2

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5. MTALHAHASSAN2

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6. MTALHAHASSAN2

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7. mathstudent55

The first step is to factor the left denominator. Can you do that?

8. anonymous

that's not one of the answers want me too post them?

9. MTALHAHASSAN2

10. mathstudent55

No.

11. mathstudent55

Once again, first, factor the left denominator.

12. MTALHAHASSAN2

how is it wrong?

13. anonymous

x minus 1 over the quantity x times x plus 1 1 minus x over the quantity x times x plus 1 3 minus x over the quantity x times x minus 1 x plus 2 over the quantity x times x minus 1

14. anonymous

oh so $\frac{ 2 }{ x(x+1)}$?

15. mathstudent55

This problem is a subtraction of fractions. We need a common denominator. The way to find a common denominator is to first factor all denomiators. $$\Large \dfrac{ 2 }{ x^2+x }-\dfrac{ 1 }{ x }$$ Factor the left denominator. Correct. $$\Large =\dfrac{ 2 }{ x(x+1) }-\dfrac{ 1 }{ x }$$

16. mathstudent55

Now you need to find the LCD of x(x + 1) and x.

17. anonymous

so x(x+1) is the lcd so multiply 1/x by x+1?

18. mathstudent55

Correct. Multiply 1/x by (x + 1)/(x + 1) $$\Large =\dfrac{ 2 }{ x(x+1) }-\dfrac{ 1 }{ x } \times \dfrac{x + 1}{x + 1}$$

19. anonymous

now what

20. mathstudent55

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

21. mathstudent55

Now do the actual subtraction. Write a new fraction with the common denominator, and subtract the numerators. Remember to enclose the second numerator in parentheses.

22. MTALHAHASSAN2

@mathstudent55 huh i goted

23. anonymous

x-1/x(x+1)?

24. MTALHAHASSAN2

so first you have to factor that x square

25. mathstudent55

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

26. mathstudent55

Numerator is either 1 - x or -x + 1, not x - 1

27. anonymous

Sweet! That's one of the answers! THANK YOU I GET IT :)!!

28. mathstudent55

The first step was factoring x^2 + x

29. mathstudent55

Great. You're welcome.

30. MTALHAHASSAN2

@mathstudent55 nice work!!

31. mathstudent55

Thanks.