The Art of Simplifying Rational Expressions

The concept of simplifying rational expressions can be understood only after the studying the basics. Once the basics are clear, it becomes very easy to solve these. The concept of solving algebraic equations can also be learnt from these basics.

Once this is understood simplifying algebraic expressions can be very simple. Basic algebraic expressions will contain the arithmetic operations of addition, subtraction, multiplication and division. They also contain constants and variables. The value of constants does not change throughout and the value of the variables can change. This is the basic difference between the two.

To simplify rational expressions one must understand what the definition of these expressions is. These can be written with the fractions. The denominator in the fraction must not be zero; otherwise it is difficult to define the fraction.

The degree of the expression plays a very important role in deciding the method to solve the expression. The question how to simplify rational expressions can be understood only if the basics are understood. It is important to learn the concept of polynomials to understand this concept. Ratio of the polynomials can be treated as an expression representing the concept. The concept of ratio is very clear and simple to understand.

There can be various terms in the polynomial. These terms can be rational or need not be rational in nature. But this will be true only for the real numbers. The complex numbers do not come into the picture here. The complex numbers consist of a real part and an imaginary part in them.

So, this cannot become a part of the polynomials that appear in the ratio. The polynomial that appears in the denominator must not be reducible to zero otherwise the whole expression is valid.This concept is also useful in geometry. The expression can be represented graphically. Simplifying these fractions can be learnt from the simplification of simpler fractions. The process in simplification is very simple.

The common terms that are present in both the numerator and the denominator are cancelled, so that the common terms do not appear twice. This is the basic idea of simplification. The same process is followed in simplifying these expressions as well. The polynomials must be reduced into simpler terms. If there are any common terms in the numerator and the denominator they must be cancelled. This makes the term simpler and easy to understand.