# Thread: Why is this statement true?

1. ## 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

2. ## Re: Why is this statement true?

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.

3. ## Re: Why is this statement true?

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

4. ## Re: Why is this statement true?

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*}.

5. ## Re: Why is this statement true?

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