• May 27th 2008, 04:40 PM
jasmine7
Can someone help me?
Please, I'm really confused. Anyone help would be appreciated.
I'm not really sure what to do w/ the x's in the equation....

heres the link to the equation:
http://img100.imageshack.us/img100/57/mathpi8.png
• May 27th 2008, 04:57 PM
Jonboy
have no fear :)

$x + \frac{1}{x} = \frac{3}{x} + 3$

Just multiply both sides by x (just the simple multiplication property):

$x[x + \frac{1}{x}] = [\frac{3}{x} + 3]x$

Distribute: $x\cdot x \,+ \not x\cdot\frac{1}{\not x} = \not x\cdot \frac{3}{\not x} + 3\cdot x$

Simplify: $x^2 + 1 = 3 + 3x$

Rearrange to standard form: $x^2 -3x - 2 = 0$

You should get $x = \frac{3}{2} \pm \frac{\sqrt{17}}{2}$.
• May 27th 2008, 07:49 PM
CaptainBlack
Quote:

Originally Posted by Jonboy
have no fear :)

$x + \frac{1}{x} = \frac{3}{x} + 3$

Just multiply both sides by x (just the simple multiplication property):

$x[x + \frac{1}{x}] = [\frac{3}{x} + 3]x$

Distribute: $x\cdot x \,+ \not x\cdot\frac{1}{\not x} = \not x\cdot \frac{3}{\not x} + 3\cdot x$

Simplify: $x^2 + 1 = 3 + 3x$

Rearrange to standard form: $x^2 -3x - 2 = 0$

You should get $x = \frac{3}{2} \pm \frac{\sqrt{17}}{2}$.

To get large brackets in LaTeX tou can use "\left[ ... \right]", these will be adaptive and give the right sized brackets for what is between, or "\big[ ... \big]"
or "\Big[ ... \Big]", "\bigg[ ... \bigg]", "\Bigg[ ...\Bigg]".

So using each of these we have:

$x\left[ x + \frac{1}{x} \right] = \left[ \frac{3}{x} + 3 \right] x$

$x \big[ x + \frac{1}{x} \big] = \big[ \frac{3}{x} + 3 \big] x$

$x \Big[ x + \frac{1}{x} \Big] = \Big[ \frac{3}{x} + 3 \Big] x$

$x \bigg[ x + \frac{1}{x} \bigg] = \bigg[ \frac{3}{x} + 3 \bigg] x$

$x \Bigg[ x + \frac{1}{x} \Bigg] = \Bigg[ \frac{3}{x} + 3 \Bigg] x$

RonL