Divide (2x)/(1-2x)

Reorder ${\displaystyle 1}$ and ${\displaystyle -2x}$.

Set up the polynomials to be divided. If there is not a term for every exponent, insert one with a value of ${\displaystyle 0}$.

Divide the highest order term in the dividend ${\displaystyle 2x}$ by the highest order term in divisor ${\displaystyle -2x}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle 2x-1}$

After changing the signs, add the last dividend from the multiplied polynomial to find the new dividend.