# Why is this statement true?

• Jan 31st 2013, 11:32 AM
Assassinbeast
Why is this statement true?
Hello folks :)

Can anybody give me a step by step of why this statement is true?

Code:

(x^2 + 4x)/x = x + 4
• Jan 31st 2013, 12:17 PM
ebaines
Re: Why is this statement true?
Quote:

Originally Posted by Assassinbeast
Hello folks :)

Can anybody give me a step by step of why this statement is true?

Code:

(x^2 + 4x)/x = x + 4

Step by step:

$\displaystyle \frac {x^2 + 4x} x = \frac {x^2} x + \frac {4x}x = x ( \frac x x) + 4 ( \frac x x ) = x(1) + 4(1) = x + 4$

Note that $\displaystyle x \ne 0$, or else the fractions are undefined.
• Jan 31st 2013, 12:32 PM
Assassinbeast
Re: Why is this statement true?
Quote:

Originally Posted by ebaines
Step by step:

$\displaystyle \frac {x^2 + 4x} x = \frac {x^2} x + \frac {4x}x = x ( \frac x x) + 4 ( \frac x x ) = x(1) + 4(1) = x + 4$

Note that $\displaystyle x \ne 0$, or else the fractions are undefined.

woooow, thank you so much man!! i wish it was written in my math book
• Jan 31st 2013, 02:48 PM
Prove It
Re: Why is this statement true?
Quote:

Originally Posted by Assassinbeast
Hello folks :)

Can anybody give me a step by step of why this statement is true?

Code:

(x^2 + 4x)/x = x + 4

Or even easier...

\displaystyle \displaystyle \begin{align*} \frac{x^2 + 4x}{x} &= \frac{x \left( x + 4 \right)}{x} \\ &= x + 4 \end{align*}

This is of course provided that \displaystyle \displaystyle \begin{align*} x \neq 0 \end{align*}.
• Feb 1st 2013, 11:42 AM
Assassinbeast
Re: Why is this statement true?
Quote:

Originally Posted by Prove It
Or even easier...

\displaystyle \displaystyle \begin{align*} \frac{x^2 + 4x}{x} &= \frac{x \left( x + 4 \right)}{x} \\ &= x + 4 \end{align*}

This is of course provided that \displaystyle \displaystyle \begin{align*} x \neq 0 \end{align*}.

Thank you too man!! thats some cool tricks :D