Algebra: How To Simplify Algebraic Fractions

Introduction

If you clicked on this blog post, you are probably looking for helpful tips in simplifying algebraic fractions.

We’ve got you covered!

We previously talked about expanding and factorising algebraic expressions. Click on the link if you missed out on that!

But in this blog post, we will share a detailed guide to simplifying algebraic fractions, along with a recap on adding fractions with the same and different denominators.

Let’s Take A Look At This Algebra Question

Here, you will see four parts of addition and subtraction of fractions (one involves a combination of both).

Before we proceed, read the instructions. You are asked to simplify the algebraic fractions.

🤔 What Does Simplifying Algebraic Fractions Mean? 🤔

When you are asked to add or subtract algebraic fractions, simplifying means that your answer must be in the form of a single fraction.

How can you do this?

Let us recap the things you learned in primary school. How do you add algebraic fractions with the same denominators like the ones below?

Do you take 2+1/5+5 and then get 3/10?

This is the wrong way to do this! What is the correct way of doing this then?

💡 How To Add Algebraic Fractions With The Same Denominators? 💡

First, check for the common denominator. In our example, both are 5 so they are the same. Because they have a common denominator, you just add the numerators and copy the denominators.

2 + 1 = 3

Therefore, the answer is 3/5.

You might also be wondering now how to add algebraic fractions with different denominators so let us try solving this:

1/2 + 2/3

Are you going to take 1+2/2+3 to get 3/5? No! This is not the correct way of doing this.

First, find the Least Common Multiple (LCM) of the denominators.

🧐 What Is The Least Common Multiple (LCM)? 🧐

It is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder.

What is the LCM of the denominators 2 and 3?

Their LCM is 6!

The first fraction then becomes 3/6 and the second becomes 4/6.

3/6 + 4/6 = 7/6 or 1 1/6

If you were not able to follow, don’t worry as we will discuss it in detail below.

Now that we’ve refreshed your memory on how to add algebraic fractions, we can proceed with simplifying algebraic fractions!

Let’s Solve Part (A)

First, check for the common denominator. Since both are 5, we can proceed with adding the numerators.

2x + x = 3x

Therefore, the answer is 3x/5.

Answer For Part (A)

3x/5 

Let’s Solve Part (B)

Again, we have to check for common denominators first. We have 18 and 12. Are they the same? No!

So, we have to find their LCM.

Their LCM is 36. Now, we will convert your algebraic fractions to upon 36.

Remember that your teachers might be very particular with presentation so follow these steps.

We multiplied our first denominator by 2 to get our LCM. Let us put brackets and multiply the numerator and denominator by 2.

For your second fraction, we multiplied our denominator by 3 to get the LCM. Put brackets and multiply our numerator and denominator by 3.

The next step will be to expand your numerators.

For the first fraction, we are going to have 14x+8. For the second fraction, we’ll have 15.

Now we have the same denominators, so we can proceed with adding our numerators.

Answer For Part (B)

Let’s Solve Part (C)

First, check if the denominators are the same.

They are not! So we have to find their LCM.

The LCM of 6 and 9 is 18. Now, we can convert our algebraic fractions to upon 18.

We multiplied our denominator by 3 to get our LCM. So let us put brackets and multiply our numerator and denominator by 3.

For our second fraction, we multiplied the denominator by 2 to get our LCM. Let us put brackets and multiply the numerator and denominator by 2.

Now, we can expand our fractions. For the first numerator, we’ll have 9x – 3. For the second numerator, we’ll have 4x – 2.

The denominators are now the same so we can proceed with subtracting our numerators.

When you are subtracting more than one term, remember to put brackets like below.

Next, copy the numerators and don’t forget to include the brackets.

Now, let us expand our numerator. Collect your x (highlighted in blue). Then, collect your numbers (highlighted in yellow).

Answer For Part (C)

Let’s Solve Part (D)

The first step you have to do is to convert 2 into a fraction. 2 is actually upon 1.

Now, you have to find the LCM of 1, 2 and 3.

The LCM of 1, 2 and 3 is 6!

The next step is to convert all the fractions to upon 6.

We multiplied our first denominator by 6 to get the LCM. Let us put brackets and multiply the numerator and denominator by 6.

Next, we multiplied our second denominator by 3 to get the LCM. Let us put brackets and multiply our numerator and denominator by 3.

Lastly, we multiplied our last denominator by 2 to get the LCM. Let us put brackets and multiply our numerator and denominator by 2.

Because our fractions have the same denominator now, we can start solving them. There’s a minus sign so remember to put brackets. Let us now expand.

Next, collect all your numbers (highlighted in yellow) and your x terms (highlighted in pink) and you will get the final answer.

Answer For Part (D)

Conclusion

I hope that after reading this blog post, you have recapped how to solve algebraic equations involving fractions with the same and different denominators.

Always remember to show a detailed presentation of your solution to avoid losing marks.

Keep on checking for more blog posts that help you tackle challenging Algebra questions.