Factoring To Find Common Denominators For Rational Expressions

In algebra, a rational expression is one that contains a polynomial function in its numerator and denominator. Having a good command of the fraction rules is very important for being a student. Likewise, rational expressions are also the form of algebraic expressions. An online rational expressions calculator by calculator-online.net helps you in determining the simplified form of the rational expressions. Also, this free rational equation calculator factors out common denominators to reduce an expression to its most generic form.

In this article, I will be discussing the proper method of figuring out the least common denominators in a rational expression with the help of factorization.

Let’s dive into it!

Factorization Of A Rational Expression:

Suppose we have the following generic rational expression:

$$ \frac{\left(x+1\right)^{2}}{x\left(x+3\right)} * \frac{1}{\left(x+3\right) $$

When we see this function’s generic form, we will notice that two terms are coming in the denominator which is common while factoring the whole expression. These two terms are \(x\) and\(\x+3\). So these will be the least common denominator of rational expression. 

Well, it may seem a little bit but believe me, a rational expressions calculator can assist you in getting rid of such difficulty in computations. Isn’t it a great thing? Yes, it is!

How To Simplify Rational Expressions?

Let me solve an example to make your vision better regarding rational expression factorization:

Problem:

Factorize the following rational expression by figuring out LCD.

$$ \frac{2}{\left(x^{2} + 6x + 9\right)} and \frac{2}{3x + 9} $$

Solution:

Here you can write the expression \(x^{2} + 6x + 9\) in its lowest form which is as follows:

$$ \left(x+3\right\) \left(x+3\right\) $$

$$ \left(x+3\right)^{2} $$

For 3x+9, we have:

$$ 3x+9 = 3\left(x+3\right) $$

Now if you see both of the simplified expressions, you will notice that two factors are appearing in the denominator of each expression. These factors are 3 and \(x+3\). This is why the least common denominator is given by the following:

$$ 3\left(x+3\right)^{2} $$

rational expressions calculator provides you with another edge of solving such expressions in a glimpse of an eye.

Using Rational Expressions Calculator:

The free-to-use rational number calculator helps you to resolve any complex algebraic expression instantly and accurately. Let me guide you on the proper use of this free calculator:

  • Write down the numerator and denominator of each fraction
  • Select the operation that you want t to simplify the given expression with
  • Tap the calculate button
  • This is how the calculator straight away displays detailed calculations and answers on the screen

Wrapping It Up:

Taking out the least common denominator from rational expressions is very handy as it takes out the complexity involved in the problem. In this article, I discussed the use of rational expressions calculators in resolving complex rational polynomial functions. I hope I will help you people a lot!

Good Luck!

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