In the same way as multiplication was the same for rational
expressions as for rational numbers so is the division of rational
expressions the same as division of rational numbers. Remember that
division of fractions of rational numbers is the same as
multiplication by the reciprocal of the divisor.
A polynomial divided by a monomial or a polynomial is also an
example of a rational expression and it is of course possible to
divide polynomials as well. When you divide a polynomial with a
monomial you divide each term of the polynomial with the
When you divide polynomials you may have to factor your
polynomials to find a common factor between the numerator and the
When there are no common factors between the numerator and the
denominator or if you can't find the factors you can use a longer
division process to simplify the expression.
You begin by dividing the first term of the dividend
(7x2) with the first term of the divisor (x) to find the
first term of the quotient (7x) and then you multiply the quotient
term with the divisor and subtract.
To find the next term of the quotient you just divide the first
term of the remaining dividend (8x - 8) with the first term of the
This means that:
Video lesson: Simplify the rational