# Can someone explain why this simplification works?

https://i.stack.imgur.com/bOLuF.png

I don't understand wouldn't -x+x cancel out to become 0?

• $-x+\frac x 2$ is not the same as $\frac {-x+x} 2$. – Kavi Rama Murthy Mar 4 at 6:09
• By that thought, are you suggesting that $1-\frac1{1000}=0$? – Andrew Chin Mar 4 at 6:09
• What $x$? You don't have an $x$. You have $\frac x 2$ or one-half of an $x$. – fleablood Mar 4 at 6:26
• Consider $1 - \frac 12$. The $1 -1$ don't cancel and become $0$ because you don't have $1-1$. The $1$ is the numerator of a fraction and not a whole number at all. This is the exact same thing $-x +\frac x2$ then you don't have $-x +x$. Then $x$ is the numerator of a fraction and not a whole value of $x$ and all. It is half of a value of $x$. It's is exaclty the same $1- \frac 12 \ne \frac {1-1}2$ and $-x +\frac x2 \ne\frac {-x + x}2$. Indeed the $\frac x2$ is one half of $x$. and $-x +\frac x = -x + \frac 12x$. – fleablood Mar 4 at 6:34

Just check that $$x-\dfrac{x}{2}=\dfrac{\color{red}{2}x}{\color{red}{2}}-\dfrac{x}{2}=\dfrac{x}{2}.$$