# STEPS to Solve simple equation

• Sep 13th 2010, 08:16 AM
neilthomason
STEPS to Solve simple equation
I have an equation and answer but do not know the steps involved to arrive at the answer. Try as I might I do need help!!

1 / x = x / 1 + x

Solving for x

x = (1+ sqrt. {5}) / 2

Is it a linear equation?
• Sep 13th 2010, 08:21 AM
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Quote:

Originally Posted by neilthomason
I have an equation and answer but do not know the steps involved to arrive at the answer. Try as I might I do need help!!

1 / x = x / 1 + x

Solving for x

x = (1+ sqrt. {5}) / 2

Is it a linear equation?

Please learn order of operations and parentheses.

"1 / x = x / 1 + x" means "1 / x = (x / 1) + x" which I'm quite sure isn't what you meant.

$\dfrac{1}{x}=\dfrac{x}{1+x}$

cross multiply and you get a quadratic.
• Sep 13th 2010, 08:33 AM
neilthomason
Thanks you are quite correct I did not mean this, I am looking for your definition (Image) of the equation.

A man once said that we are all ignorant.......... but not about the same things.

What will the quadratic look like?
• Sep 13th 2010, 08:39 AM
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Quote:

Originally Posted by neilthomason
What will the quadratic look like?

It will look like this. :)

Golden ratio - Wikipedia, the free encyclopedia
• Sep 13th 2010, 08:41 AM
e^(i*pi)
Quote:

Originally Posted by neilthomason
Thanks you are quite correct I did not mean this, I am looking for your definition (Image) of the equation.

A man once said that we are all ignorant.......... but not about the same things.

What will the quadratic look like?

First of all we know that $x \neq 0, -1$

Second, multiply each side by the others denominator: $\dfrac{1}{x} \cdot \dfrac{1+x}{1+x} = \dfrac{x}{1+x} \cdot \dfrac{x}{x}$ (we can do this because of what I defined above)

When we simplify we get: $\dfrac{1+x}{x(1+x)} = \dfrac{x^2}{x(1+x)}$

The denominators are the same and hence will cancel to give $1+x = x^2$ - put into standard form and use the quadratic formula to solve