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What Is A Rational Algebraic Expression?

An expression that can be represented with the help of polynomials written in fractions is known as the algebraic rational expression. There can be many ways to resolve an algebraic rational expression to its simplified form. But factoring is considered the best and easiest among all. Also an online rational expressions calculator is also here to help you people in reducing such complex polynomial expressions. Is it not a great offer for you if you are a scholar? I think you must think about it again.

Anyways, in this technical content, I will be covering some detail on algebraic rational expressions and easy ways to reduce them.

Stay focused!

Arithmetic Operation Algebraic Expressions:

Just like you apply various mathematical operations on the simple fractions, you need to apply those same operations on the algebraic expressions too. It will lead you to know how to simplify rational expressions. The only addition is that the variables are not involved in simple fractions while they are present in the case of polynomial expressions. Let us discuss them in some detail:


You can add two or more algebraic rational expressions with the help of the free rational number calculator. But when it comes to the manual calculations, you need to keep in mind the following terms and conditions:

  • Write all rational expressions along with an addition sign among them
  • Take a common denominator
  • Now write down the factors in the numerator and add them to unite
  • At last, you will obtain the simplified addition form of the rational expression.

The interesting fact here is that you can also do so with the help of the free online rational expressions calculator immediately and with up to 100% accuracy. I know you must be thinking that how could it be possible? But believe me, it works!


As you already know that subtraction is nothing but considered as the opposite operation to that of the addition. So follow the points given below to subtract rational expressions:

  • Simply write the rational expression in the standard form having a subtraction sign among them
  • After doing so, take out common denominators and add subtract all the numerator terms above the fraction
  • Finally, cut the similar terms with opposite signs to reduce the expressions


Multiplication is a little bit challenging every time. But do not worry at all as the free rational equation calculator will be helping you people always in reducing multiplication problems regarding rational expressions. But when it comes to manual calculations, you definitely need hands-on practice. Let me guide you how to do it:

  • Write down rational fractions having a multiplication sign in among.
  • Multiply the numerator and denominator terms separately
  • After doing so, write down the expressions in the numerator and denominator in descending powers
  • This is how you make it a simplified expression


Just like subtraction and addition, division is also a reciprocal operation of the multiplication. Here what is mandatory includes:

  • Write the rational fractions with division signs among them
  • Leave the first fraction and change division sio=gn of the rest terms inti multiplication sign
  • Also, exchange numerators and denominators of these terms
  • Repeat the multiplication process to get the simplified form.

Wrapping It Up:

In this article, I discussed various operations on the algebraic rational expressions to reduce them to most simple forms. Also the use of free rational expressions calculators has been enlightened again and again for the sake of your ease.