What is the solution to this algebraic problem?

[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)

 

[Hurkyl]

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?

 

[xxpsychoxx]

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?

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

 

[Hurkyl]

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?

 

[xxpsychoxx]

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

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

 

[Hurkyl]

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

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

 

[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?

 

[Hurkyl]

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?

 

[xxpsychoxx]

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

I'm unsure about the other method

 

[Hurkyl]

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)

 

[xxpsychoxx]

Oh ok, i thought that was a typo

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

 

[Hurkyl]

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!

 

[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

 

[Hurkyl]

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.

 

[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?

 

[Hurkyl]

13x doesn't look right

 

[xxpsychoxx]

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

Oops sorry that's 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