## tafkas77 2 years ago Simplifying complex fractions.... Help!

1. tafkas77

The equation looks like this: |dw:1363123735015:dw|

2. tafkas77

@zepdrix can you help me, please?

3. zepdrix

$\large \frac{\left(\dfrac{4}{x+3}\right)}{\dfrac{1}{x}+3}$Does this look accurate? :) I added the brackets so we can see which one is the fraction on top of the fraction :P

4. tafkas77

Aha! Yes, it's perfect. :)

5. zepdrix

Let's start by multiplying by $$\large \dfrac{x}{x}$$.$\large \frac{\left(\dfrac{4}{x+3}\right)}{\dfrac{1}{x}+3}\left(\frac{x}{x}\right)$

6. zepdrix

Understand where to put the x within the brackets?

7. zepdrix

We can think of it like this, $\large \frac{\left(\dfrac{4}{x+3}\right)x}{\left(\dfrac{1}{x}+3\right)x}$

8. tafkas77

I believe so.... I'll end up with... 4x/3 for the top fraction? And 1 + 3x for the bottom fraction?

9. tafkas77

wait...

10. tafkas77

4x/ x^2 + 3x

11. zepdrix

$\large \frac{\left(\dfrac{4x}{x\color{orangered}{+3}}\right)}{\left(1+3x\right)}$Hmm you were on the right track with your first guess :) you just missed this little orange part. See how the top x is multiplying the 4, and the bottom one multiplied both terms.

12. zepdrix

Woops I did the wrong portion in orange, my bad

13. tafkas77

I see my mistake... :) So was my second guess right? I changed my answer to $\frac{4x }{ x^2 + 3x }$ while you were typing, sorry. :)

14. tafkas77

I didn't put it into 'fancy' form, though. :)

15. zepdrix

$\large \frac{\left(\dfrac{4x}{x+3}\right)}{\left(1+3x\right)} \qquad = \qquad \frac{4x}{(x+3)(3x+1)}$This part make sense? :o

16. tafkas77

yes; I see what you did. But how come the denominator of the first fraction isn't x^2? Why is it only "x"... we multiplied the x's, right?

17. zepdrix

Sorry for the delay :c I couldn't connect to the site for a bit there.

18. zepdrix

|dw:1363126766341:dw|

19. zepdrix

|dw:1363126871122:dw|

20. zepdrix

The top multiplication looks like this,$\large \left(\frac{4}{x+3}\right)x$Which we can think of as,$\large \left(\frac{4}{x+3}\right)\frac{x}{1}$Understand why it doesn't produce an x^2 in the bottom? :O We're not multiplying the x+3 by anything.

21. tafkas77

okay, I understand. Thank you for explaining that to me! :D I'm sorry it took me so long - the site wasn't working! Okay, so after I do all that, I got this as my answer: $\frac{ 4x }{ 3x^2 + 10x + 3 }$ Is that right?

22. danielcvalencia

Welcome to OpenStudy, @tafkas77 !

23. tafkas77

@danielcvalencia Hee hee, thanks! :D But I am not new to OS! :) I have a 65 SmartScore - I've been here for a little while. This is just my first question in Algebra, not my first question ever. But I appreciate your kindness very much! :)

24. zepdrix

yah looks right c: good job.