Divide ((x-5)/5)÷((x-2)/3)

Split the fraction ${\displaystyle \frac{x-5}{5}}$ into two fractions.

Split the fraction ${\displaystyle \frac{x-2}{3}}$ into two fractions.

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 ${\displaystyle \frac{x}{5}}$ by the highest order term in divisor ${\displaystyle \frac{x}{3}}$.

Multiply the new quotient term by the divisor.

The expression needs to be subtracted from the dividend, so change all the signs in ${\displaystyle \frac{x}{5}-\frac{2}{5}}$

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