Factoring To Find Common Denominators for Rational Expressions

Rational expressions can be defined as fractions, in which the numerator and denominators are polynomials, in simpler terms, the ratio between two polynomials. One method we’re going to discuss is the factoring method of Rational numbers.

Factoring is a method in mathematics that helps break it down into smaller numbers. Once multiplied with one another, the original number is obtained.

The factoring method is standard in the subjects of mathematics that helps in resolving problems related to numbers. The factoring method is used in mathematics at every level as it provides a standardized method for solving quadratic expressions and simplifying complex expressions. It is the opposite of the expanding method.

How to Simplify Polynomials:

Polynomials are expressions that consist of more than two algebraic terms. The rational expressions calculator helps in displaying the rationalized form of a given expression. Other than that, a rational equation calculator can come into use for a step-by-step solution of the expression. Both of the calculators can be found free online and are fast and easy methods for mathematical expressions.

Finding Common Denominators:

In simple terms, a common denominator would be defined as a number with a similar theme to the several fractions in a mathematical expression. How to find a common denominator in rational expressions?

To find common denominators in a given expression, we use the factorization method. This method is used to find the least common denominator (LCD). The LCD is the smallest multiple that is common amongst the denominators. The expressions are factorized then the distinct factors are multiplied.

Example:

Let’s take an example that will help us understand the expressions more in-depth:

(×+1) (×+2) and (×+2) (×+3)

The LCD of the given an example would become:

(×+1) (×+2) (×+3)

Once the LCD is known, each expression is multiplied by one such that the denominators are equal to the LCD. This will lead us to find the common factors.

Like in the provided example

(×+1) (×+2) will be multiplied by (×+3) ÷ (×+3)

While (×+2) (×+3) will be multiply by (×+1) ÷ (×+1)

Restrictions:

When there are restrictions highlighted in the expression, the denominator is set to be equal to zero. It is then solved by being denoted as x. If the expression consists of an even root, the radicand is more significant than or equal to zero.

The expression is then to be solved, and the solutions obtained are the restricted values. Restrictions can and are overcome by different methods such as the usage of online tools like rational expressions calculators and rational equation calculators.

Conclusion:

Expressions are combined in the numerator once the denominators are equal and turned into a single rational expression by subtracting or adding the numbers. The numerator will be divided by the denominator and will be rewritten.

The expression is thus simplified once the common denominator is found through the process of factorization. The online tools have made it easier for one to find solutions, whether it be just the end solution or the in-depth, and step-by-step analysis method.