Is $\frac{4x + 2}{12 x ^2}$ simplifiable?

Question

I'd like to know what methods can I apply to simplify the fraction $\frac{4x + 2}{12 x ^2}$

Is it valid to divide above and below by 2? (I didn't know it but Geogebra's Simplify aparantly does this)

Thanks in advance

Answer 1

Factor out the $2$ from both the numerator and denominator. That is, $$\require{cancel}\frac{4x+2}{12x^2}=\frac{\cancel{2}(2x+1)}{\cancel{2}\cdot6x^2}=\frac{2x+1}{6x^2}.$$

Answer 2

Yes, you are multiplying by $1$ in the form $\dfrac {\frac 12}{\frac 12}$, which takes you to $\frac {2x+1}{6x^2}$ That is all you can do

Answer 3

You can factor out a two from the numerator and denominator to get $$\frac{2x+1}{6x^2}.$$ multiplying the numerator and the denominator by the same number will never affect the value of the fraction.

Answer 4

If you are looking for a formula that can be evaluated with a minimal number of bit operations for any given $x$, it might be best to multiply by $\frac{\frac14}{\frac14}$ and get $$\frac{x+\frac12}{3x^2}$$ which in binary would be $$\frac{x+0.1}{11\cdot x^{10}}$$