Mathematics - Algebric Fractions

Algebraic fractions refer to the one that has polynomials in the denominator. The denominator cannot be 0. Each polynomial can be written as an Algebraic fraction with a Denominator. We formulate algebraic fractions as we address simple fractions with a numerator and denominator.

The difference between a normal fraction and an algebraic fraction is that the normal fraction normally includes numbers in numerator or denominator. Conversely, algebraic fractions have expressions in both the numerator and denominator form. Algebraic fractions are rational expressions that can be written in the following fractional form:

rac {P (x)}{Q(x)} where Q(x) eq 0

Let us see some of the arithmetic operations performed in Algebraic expressions.

1. Adding Algebraic Fractions

We use L.C.D to combine two or more algebraic fractions when adding and subtracting between them. L.C.D or Least common denominator has a simple process. Just like LCM, LCD is performed. It shows the smallest number, which is divisible by the denominator of each fraction in the question.

2. Subtracting Algebraic Fractions

We identically subtract Algebraic fractions when adding them. The only exception is when we apply the method of subtraction after multiplication. The symbols of all the factors within the brackets are modified because of the minus sign outside the bracket.

3. Multiplying Algebraic Fractions

Multiplying algebraic fractions is very easy. You have to multiply the numerator with the numerator and the denominator with the denominator.

4. Dividing Algebraic Fractions

We divide algebraic fractions practicing the same method, i.e. we take reciprocal of the second fraction.

Why do we simplify fractions?

Algebraic fractions are expressed in a simple form. For example, if it is 1, it is the only common factor of its Numerator and Denominator. Therefore, simplification of the fraction is necessary because it is easy to calculate in a simple form. Let us proceed further and have a look at how the simplification of Algebraic fractions is done.

How do you simplify algebraic fractions?

  • At first, check out if you have to multiply, add, subtract, or divide.
  • Multiply the denominators to get the same denominator.
  • Multiply the first numerical fraction by the second denominator to get the first numerator.
  • Multiply the second numerical fraction by the first denominator to get the second numerator.
  • To get the answer, add, subtract, multiply, or divide the numerator, then divide by the denominator in step 2.
  • Simplify the fraction if divisible.

The complex questions may seem hard, but once you understand the essential details, such as factorization, it becomes easy to solve.

You can also use the least common divisor where applicable or the greatest common denominator. After multiplication, you can expand the problem to simplify the question.