## anonymous one year ago Hey! I really need help on this :( I will fan and medal. Using the equation below as a model, fill in numbers in the place of a and b to create a rational equation that has an extraneous solution. (x + a)/ax = b/x Part 1. Show all work to solve for x in the equation and check the solution. Part 2. Explain how to identify the extraneous solution and what it means.

1. anonymous

@Vocaloid

2. anonymous

I don't necessarily want an answer I just want someone to work it out with me :)

3. netlopes1

$\frac{x+a}{ax}=\frac{b}{x}\rightarrow Is \quad this?$

4. anonymous

Um, I think you're asking me what values I plugged in for a and b. Here: a = 3 and b = 1.

5. netlopes1

First, remember, "x" must be different of zero, ok?

6. anonymous

Ok :) so that means if I work it out for x and it comes out to x = 0 then it is not a solution, correct?

7. netlopes1

If x=0, both denominators of fractions become null and the equation will be indefined, or better, there is no solution.

8. netlopes1

Item "I.", ok? $\frac{x+a}{ax}=\frac{b}{x}\rightarrow \frac{x+a=ab}{ax} \rightarrow$Do you understand so far?

9. anonymous

No, I'm sorry but I do not understand... Also, my question says that I need to come up with some values for a and b. So, I think I might need to put those values in before I start working it out :) my values are: a = 3 and b = 1

10. netlopes1

Why your values are a=3 and b=1? These values are in the question.... but if "yes", it's simpler... replace these values in the equation, directly... look

11. netlopes1

$\frac{x+a}{ax}=\frac{b}{x}\rightarrow \frac{x+3}{3x}=\frac{1}{x} \rightarrow$

12. anonymous

@itsdaniela @raiders88 @Twetapoo @bishop.courtney2014 @Hero @amistre64 @ganeshie8 @saifoo.khan @paki @wio @Preetha

13. anonymous

Ok :)

14. netlopes1

And solve the equation for x

15. anonymous

But I still do not know how to figure that out. I guess cross multiply?

16. anonymous

@IrishBoy123

17. netlopes1

Yes, look: $\frac{x+3}{3x}=\frac{1}{x} \rightarrow x(x+3)=3x.1 \rightarrow ok?$

18. anonymous

Ok, so I would come out with x^2 + 3x = 3x?

19. anonymous

But then it would be x^2 = 0... I don't think that is correct.

20. netlopes1

This is the cross multiply, ok? So, if x^2 +3x = 3x, or ??? Look

21. anonymous

I don't understand. I think you subtract the 3x from each side...

22. anonymous

Which would leave you with x^2 = 0 but then you can't take the square root of 0 so I'm not sure what to do next. But is that what extraneous means?

23. netlopes1

Remember, when I said that "x" must be different of zero? And now, your solução is exactly zero? This is an inconsistency solution, so, to a=3 and b=1, this equation has no solution.... ok.... but x^2 is a quadratic function, whose graph is a parabola, remember?

24. anonymous

Umm, I don't understand.

25. anonymous

You don't have to help me if you don't want to, I know that this is probably very frustrating. I'm sorry that I stink at math lol

26. anonymous

But thank you for your time :) I will medal :)

27. anonymous

Ok, thanks @netlopes1

28. netlopes1

Ok, but I will try again, ok?

29. netlopes1

It's no excuse, but my English is terrible (I'm Brazilian) and mathematics nomenclature is hard for me .... but I promise I will improve and I never give up ...

30. anonymous

It's fine :) I'm just not good at math. Yes! It is always good to never give up! Always try your very best :) and if you have done your best, that's all that matters. Thanks again! And I finally figured it out :)