This should be so simple??

boxfresh

New member
Joined
Jan 26, 2009
Messages
4
Hello all, was hoping i could get some advice on the following equation?

x+6 14
---- - ----- = 0
x 3x - 8

I have tried factorising the equation, but still can not solve for x

many thanks :(
 
the equation did not look how intended, should be;

(x+6 / x) - (14/3x - 8) = 0
 
boxfresh said:
(x+6 / x) - (14/3x - 8) = 0
Your bracketing is wrong; should be (x+6)/x - 14/(3x - 8) = 0
Hint:
(x+6) / x = 14 / (3x - 8)
Now criss-cross multiplication
 
or you can multiply each term by the LCM of the denominator.

\(\displaystyle \frac{x+6}{x} \, - \frac{14}{3x-8} \, = \, 0\)

Multiply by x(3x-8), to get,

\(\displaystyle {(x+6)}\cdot{(3x-8)} \, - {14}\cdot{x} \, = \, 0\)

Now simplify and you'll get a quadratic equation - solve by your favorite method.
 
Denis said:
Hint:

(x+6) / x = 14 / (3x - 8)

Now criss-cross multiplication


I just referenced this thread as an example of cross-multiplication, so I'm posting the following.

Cross multiplication yields:

\(\displaystyle {(x+6)}\cdot{(3x-8)} \, - {14}\cdot{x} \, = \, 0\)

 
Thanks for the help!
Once cross multiplied and simplified, i came across a quadratic equation.
By solving this i came to x=0 in both cases?
Is this correct?
 
boxfresh said:
By solving [a quadratic equation I,] came to x=0 in both cases? Is this correct?


Nope.

One solution is close to -3, and the other is close to 5.

You might save yourself some response time by posting your work.

What is the quadratic equation that you got?

 
Brilliant, i thought it was wrong? :?

Let me explain what i have done, and it may explain where i have gone wrong;

(x+6).(3x-8)-14x = 0

which becomes;

3x^2 + 10x - 48 - 14x = 0
collect common toggether;
3x^2 - 4x - 48 = 0
This is the quadratic equation that i have input into the standard quadratic equation formula, as i could not find an easy factorisation?

Does this explain where i have gone wrong?
 
box, box... If you are not in the business of considering the Domain, then you are far too likely to obtain answers that do not make sense, even if you manage to manipulate all the little symbols correctly.

Give some thought to the adding of fractions.

1/3 + 1/2 = ?? How do you do that? What about 3 and 2 leads you to a conclusion?

5/12 + 2/7 = ?? How do you do that? What about 7 and 12 leads you to a conclusion?

You have (x+6)/x - 14/(3x-8) = 0 Right now, you MUST be thinking about x = 0 and 3x-8 = 0. Why is that important?

Hint: If x = 0, what happens if you multiply by x?
Hint: If x = 8/3, what happens if you multiply by (3x-8)?

AFTER these considerations, you can continue.

(x+6)/x - 14/(3x-8) = ?? How do you do that? What about x and (3x-8) will lead you to a conclusion?
 


Your quadratic equation is correct.

3x^2 - 4x - 48 = 0

Now, you need to show me how you used the Quadratic Formula.



I'll do an example, so you can see how we type it all out.

5x^2 - 15x - 12 = 0

x = [ 15 +/- sqrt(15^2 - 4(5)(-12)) ] / [2(5)]

x = [ 15 +/- sqrt(225 + 240) ] / 10

x = [ 15 +/- sqrt(465) ] / 10

MY EDITS: Fixed sign error and missing brackets (Thank you, Denis)
 
Re:

mmm4444bot said:
5x^2 - 15x - 12 = 0
x = [ -15 +/- sqrt(15^2 - 4(5)(-12)) ] / 2(5)
x = [-( -15) +/- sqrt(15^2 - 4(5)(-12)) ] / [2(5)] : go to bed with no dessert :twisted:
 
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