Algebraic fractions, like fractions in arithmetic, are divided by inverting the second fraction and then multiplying.
Example:
(8x^2/3)/[6x^3/(3x - 12)]
Step1: Change to a multiplication example;
(8x^2)[(3x -12)/6x^3]
Step 2: Factor;
(8x^2)[3(x - 4)/6x^3]
Step 3: Cancel common factors;
4(x -4)/3x
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A rational algebraic expression is the ratio of two algebraic expressions. That is, one algebraic expression divided by another. It is important that the domain is defined in such a way the the rational expression does not involve division by 0.
You divide the numerator of the rational expression by its denominator.
irrational expression is that wich are not rational or it can't be written in the form of p/q. such as (x)1/3
A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. In another polynomial is a subset of algebraic expression.
If an algebraic expression is equivalent to another algebraic expression then it is an equation.