fractional equations: [4 - (3x + 4)/4][(x+4)/(x-4) - 1 = 21

C

Chris*

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Jan 9, 2007
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I'm having a difficult time solving this equation.

[ 4 - (3x + 4)/4 ][ (x+4)/(x-4) - 1 = 21

So far I've come up to

I keep coming up with the answer as 4, but it doesn't seem to fit the equation when I check it.

Am I doing something wrong? Or is it that there is no solution?
 
Re: fractional equations

Hello, Chris*!

You're missing a bracket.
We can't read the problem . . . but I'll take a guess.

\(\displaystyle \L\,\left[4\,-\,\frac{3x\,+\,4}{4}\right]\cdot\frac{x\,+\,4}{x\,-\,4}\,-\,1\:=\:21\)
Click to expand...

We have: \(\displaystyle \L\:\left[\frac{16\,-\,3x\,-\,4}{4}\right]\cdot\frac{x\,+\,4}{x\,-\,4}\,-\,1\:=\:21\)

. . \(\displaystyle \L\frac{12\,-\,3x}{4}\cdot\frac{x\,+\,4}{x\,-\,4} \,-\,1\:=\:21\)


In the first numerator, factor out -\(\displaystyle 3\):

. . \(\displaystyle \L\frac{-3(x\,-\,4)}{4}\cdot\frac{x\,+\,4}{x\,-\,4} \:=\:22\)

And we have: \(\displaystyle \L\:\frac{-3(x\,+\,4)}{4}\:=\:22\;\;\Rightarrow\;\;-3x\,-\,12\:=\:88\)

. . \(\displaystyle \L-3x\:=\:100\;\;\Rightarrow\;\;\fbox{x\:=\:-\frac{100}{3}}\)

 
Oops! It should actually read

[ 4 - (3x + 4)/4 ][ (x+4)/(x-4) - 1]= 21

I can't believe I missed that...

P.S. How did you write the equation out like that?
 
Chris* said:
How did you write the equation out like that?
Click to expand...
The poster was using LaTeX coding. If you do a "quote", you can see his coding in the window that opens up.

You can learn more about LaTeX by following the links in the "Forum Help" pull-down menu at the very top of every forum page.

Thank you.

Eliz.
 
Hello again, Chris!

In that case, there is no solution . . .


We have: \(\displaystyle \L\:\left[4\,-\,\frac{3x\.+\,4}{4}\right]\cdot\left[\frac{x\,+\,4}{x\,-\.4}\,-\,1\right]\:=\: 21\;\;\;\text{Note that }x\,\neq\,4\)

. . \(\displaystyle \L\left[\frac{16\,-(3x\,+\,4)}{4}\right]\cdot\left[\frac{x\,+\,4\,-\,(x\,-\,4)}{x\,-\,4}\right]\:=\:21\)

. . . .\(\displaystyle \L\left[\frac{16\,-\,3x\,-\,4}{4}\right]\cdot\left[\frac{x\,+\,4\,-\,x\,+\,4}{x\,-\,4}\right]\:=\:21\)

. . . . . . . . . . . . . \(\displaystyle \L\left[\frac{12\,-\,3x}{4}\right]\cdot\left[\frac{8}{x\,-\,4}\right]\:=\:21\)

Factor: . . . . . . . . .\(\displaystyle \L\frac{-3(x\,-\,4)}{4}\,\cdot\frac{8}{x\,-\,4}\:=\:21\)

Cancel: . . . . . . . . . . . . . . . . . \(\displaystyle \L\frac{-3}{4}\,\cdot\frac{8}{1}\:=\:21\)

And we get this absurdity: . . . . . \(\displaystyle \L-6 \:=\:21\)


Therefore, the equation has no solution.

 
Thanks a lot. Now I know I'm not insane! That's actually the first answer I came up with, but I figured that couldn't be right and thought I did something wrong. Then I tried something else and came up with four and that was wrong too. :p

This problem was on a review sheet for a math test. Sheesh! My teacher what a tricky guy.
 
Chris* said:
This problem was on a review sheet for a math test....
Click to expand...
Fair warning: Expect a "no solution" exercise on the test!

Eliz.
 
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