# Algebraic Problem

1. Mar 27, 2004

### xxpsychoxx

This question kinda stumped me. Can any1 post the answer with the working and all? Thanks

Show that

$$\frac{ 3 \left( \frac{x+5}{x-1} \right) + 4 }{ 4 \left( \frac{x+5}{x-1} \right) + 1 }$$ = (3x+11)/{5x+19)

Last edited: Mar 28, 2004
2. Mar 27, 2004

### Hurkyl

Staff Emeritus
Sorry, we don't do your homework for you.

Anyways, you seem to be missing parentheses, did you mean:

$$\frac{ 3 \left( \frac{x+5}{x-1} \right) + 4 } { 4 \left( \frac{x+5}{x-1} \right) + 1 }$$

?

Anyways, what have you tried to do to solve this problem?

Last edited: Mar 27, 2004
3. Mar 27, 2004

### xxpsychoxx

Yes, thats what i meant, but i was unsure on how to write it in that format. Well first, i tried to cross multiply but thats the problem..I'm not sure how to..

4. Mar 27, 2004

### Hurkyl

Staff Emeritus
Well, in general, cross multiplication says that the equation

p/q = r/s

is equivalent to

ps = qr (with q and s inequal to 0)

Are you having trouble seeing how to make this substitution, or is it the next steps?

5. Mar 27, 2004

### xxpsychoxx

yep, it's the substitution thats giving me the problem so far

4((x+5/(x-1))+1 * 3x+11 only this one though

Last edited: Mar 27, 2004
6. Mar 27, 2004

### Hurkyl

Staff Emeritus
You have to put [ tex ] and [ /tex ] tags (no spaces) around the LaTeX code.

You're missing the ) after x + 5, but I think that's just a typo.

The big thing that you might be doing wrong is that you didn't put parentheses around each of the terms there. What you want is

$$( 4 ( \frac{x+5}{x-1} ) + 1 ) (3x + 11)$$

7. Mar 27, 2004

### xxpsychoxx

$$(4 ( \frac{x+5}{x-1} + 1 ) (3x+11)$$

hmm ok i think i got the hang of it
so can you tell me exactly how do i go about multiplying these two terms?

Last edited: Mar 27, 2004
8. Mar 27, 2004

### Hurkyl

Staff Emeritus
You're missing a parenthesis again!

There are at least two ways to progress from here.

One way is to look at the equation as a whole imagine the complicated thing is replaced by a simple thing; do you know how to expand (4z+1)(3x+11)?

The other way is to look at little pieces. Do you know any way to combine 4 (x+5)/(x-1) + 1 into one term?

9. Mar 27, 2004

### xxpsychoxx

hmmm i expanded (4x+1)(3x+11) and got 12x2+47x+11

I'm unsure about the other method

10. Mar 28, 2004

### Hurkyl

Staff Emeritus
Try the same procedure, but on (4z+1)(3x+11) instead of (4x+1)(3x+11).

(We are justified in making a new letter to represent the fraction (x+5)/(x-1), but it has to be a new letter; replacing the fraction with x won't work)

11. Mar 28, 2004

### xxpsychoxx

Oh ok, i thought that was a typo

Ok i got 12xz+44z+3x+11

12. Mar 28, 2004

### Hurkyl

Staff Emeritus
That looks right. Now, since z was a substitute for the fraction (x+5)/(x-1), if you substitute the fraction back in for z, you will have successfully multiplied the two terms you had trouble with!

13. Mar 28, 2004

### xxpsychoxx

Ohhhhh ok i see Lol i didn't think of it that way. However I am still in a bit of a jam So i'm left with:

15x-5({x+5}/{x+1}) = 12x({x+5}/{x-1}) + 44({x+5}{x-1}) + 3x + 1

Or something like that

Last edited: Mar 28, 2004
14. Mar 28, 2004

### Hurkyl

Staff Emeritus
Well, there are (at least) again two approaches. :)

(a) Combine each side into a single fraction
(b) Clear the denominators (by multiplying both sides by the least common denominator)

And I'm off to bed.

15. Mar 28, 2004

### xxpsychoxx

hmmmm, my previous equation was incorrect. Here is the correct one:

57(x+5)/(x-1) + 15x(x+5)/(x-1) +20x + 76 = 12x(x+5)/(x-1) + 44(x+5)/(x-1) + 3x + 11

Then i subtract then get:

$$13(\frac{x+5}{x-1}) + 3x(\frac{x+5}{x-1}) = -17x -65$$

=$$\frac{13x(x+5) +3x(x+5)}{x+1}$$

Any errors?

Last edited: Mar 28, 2004
16. Mar 28, 2004

### Hurkyl

Staff Emeritus
13x doesn't look right

17. Mar 28, 2004

### xxpsychoxx

$$\frac{13(x+5) +3x(x+5)}{x-1}$$

Oops sorry thats what i meant! OHHHHHHHHH YAY!! Thanks a lot ,i'm finally seeing the answer I got x is either equal to 0 or -3.8

Last edited: Mar 28, 2004
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