# How to Solve Algebraic Fractions

While algebraic fractions might seem intimidating, they are quite simple to solve if you follow certain rules. Firstly, algebraic fractions aren’t too far off from normal fractions. The only difference is that instead of numbers, you have letters. Therefore, the rules you utilise in normal fractions are exactly the same ones used for algebraic fractions.

In this article, we will explain how to solve algebraic fractions in a simple and effective manner.

## What are Algebraic Fractions?

Algebraic fractions, also often referred to as rational expressions, are fractions where the numerator and denominator are polynomials. A polynomial can be defined as a mathematical expression that consists of variables, coefficients, and/or exponents. These are combined by making use of addition, subtraction, multiplication, and division.

Algebraic fractions appear in many fields and areas of mathematics and science. Some of the areas in which you may encounter them include algebra, physics, and calculus. It is, therefore, important that you understand how they work and how to solve them.

## Simplifying Algebraic Fractions

Simplifying algebraic fractions means that you take an algebraic fraction and change it into its simplest form. Ultimately, this simplification allows you to solve fractions more easily and is, therefore, an important skill to learn.

When simplifying an algebraic fraction, the aim is to take it down to a place where the numerator and denominator have no common factors and cannot be further simplified.

To simplify an algebraic fraction, remember to always factorise the numerator and denominator. Once you have done this, you will be able to cancel any common factors. If there are no common factors, then the fraction is in its simplest form. However, in some cases, you will be able to perform another simplification by making use of other algebraic rules such as division.

## Solving Algebraic Fractions

Now that you know what algebraic fractions are and how to simplify them, we can jump into how to solve them by adding, subtracting, multiplying, and dividing them. It will be easy once you understand the concepts, we promise!

### Subtracting and Adding Algebraic Fractions

Subtracting and adding algebraic fractions is quite simple. Firstly, you must ensure that the denominators are equal before adding or subtracting can occur. Remember that the denominator is the variable below the line. Therefore, exactly the same letters (variables) must be present in both the denominators. In order to create equivalent fractions, you can multiply by variables and/or numbers when and where needed.

### Multiplying Algebraic Fractions

If you are struggling to understand the multiplication process of algebraic fractions, don't fret. To multiply an algebraic fraction, simply multiply the numerators. You can then put them over the product of the denominators.

### Dividing Algebraic Fractions

All you have to do to successfully divide an algebraic fraction is follow a few simple rules. All the rules and routines you have previously learnt remain the same! As per usual, in order to divide, you must multiply by the reciprocal. If you would like, you could even make use of cross-cancelling to simplify the fractions before making your final calculation (multiplication).

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