# Math Help - STEPS to Solve simple equation

1. ## 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?

2. 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.

3. 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?

4. Originally Posted by neilthomason
What will the quadratic look like?
It will look like this.

Golden ratio - Wikipedia, the free encyclopedia

5. 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