Algebraic fractions are fractions that have variables in them. For example, (x + 1)/(x - 2) is an algebraic fraction because it has the variable x in the numerator and denominator.
To work with algebraic fractions, we need to follow the same rules as regular fractions. We can add, subtract, multiply, and divide them, but we need to find a common denominator first. The common denominator is the same as the LCM of the denominators, which is the smallest number that both denominators can be divided into evenly.
For example, let's say we want to add the fractions (x + 1)/(x - 2) and (2x)/(x - 2). To do this, we need to find a common denominator. The denominator of the first fraction is (x - 2), and the denominator of the second fraction is also (x - 2), so we don't need to do anything. The common denominator is (x - 2).
Now, we can add the two fractions by adding their numerators and putting the result over the common denominator:
[(x + 1) + 2x]/(x - 2) = (3x + 1)/(x - 2)
So, that's the basic idea of algebraic fractions. They are fractions that have variables in them, and we can add, subtract, multiply, and divide them by finding a common denominator.