## P->Q 2 years ago 1/x^2 + 1/x =6 solve for x

1. petewe

make the left side into 1 equation.

2. asnaseer

multiply both sides by$$x^2$$ and solve the resulting quadratic equation.

3. P->Q

$x^2/ x^2 + x^2/x^2 = 6x^2$

4. P->Q

2x^2 = 6x^2

5. asnaseer

the denominator of your second term above is wrong

6. asnaseer

you should get:$x^2/ x^2 + x^2/x = 6x^2$

7. asnaseer

next - simplify each term

8. P->Q

but dont they need to have the same denominator to add

9. asnaseer

what does $$x^2/x^2$$ equal?

10. P->Q

1

11. asnaseer

correct - now simplify the next term

12. P->Q

1+ x= 6x^2

13. asnaseer

thats right - now re-arrange this into a standard form, i.e into the form $$ax^2+bx+c=0$$ and then solve

14. P->Q

so I did quadratic equation and go -1 plus or minus radical 25 all over -12

15. asnaseer

doesn't look right - can you please show your steps so that I can help spot where you may have made a mistake?

16. P->Q

k, u said put it into the standard form so I started from 1 + x = 6x^2 -6x^2 + x+1 = 0 a= -6, b= 1, c= 1 $-1\pm \sqrt{1^{2}-4(-6)(1) \over 2(-6)}$

17. P->Q

then got -1 plus or minus radical 25 all over -12

18. asnaseer

oh - sorry - I misread

19. asnaseer

you are right - and you know what $$\sqrt{25}$$ equals?

20. asnaseer

the formula you used doesn't look quite right, it should be:$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

21. asnaseer

the WHOLE thing should be divided by 2a

22. asnaseer

so you should have got:$\frac{-1\pm \sqrt{1^{2}-4(-6)(1)}}{2(-6)}$

23. P->Q

o ok so um x = 1/-3 and x = 1/2

24. asnaseer

perfect!

25. P->Q

ya I ment to put all over 2a but I was trying to make it come out nice and pretty in the equation thing but it took lng

26. asnaseer

although you should write it as: x=-1/3 or 1/2

27. asnaseer

you don't usually put the minus sign in the denominator

28. P->Q

wow these are so frustrating I was literally about to give up and go home, im in a library trying to study and there are all these other students basically hanging out and talking and there are no available tutors

29. asnaseer

also note that you should use the word "or" rather than "and" here. i.e. x = -1/3 or 1/2 instead of x = -1/3 and 1/2 because x canot equal both values at the same time

30. P->Q

ok ill do that

31. P->Q

thanks a lot you gave me a little hope to keep pushing a little more

32. asnaseer

great - and keep persevering - you'll get the hang of these very soon I'm sure :)

33. asnaseer

yw :)