Algebraic Fractions
VIDEO COMING SOON…
In this post, we’re going to be covering Algebraic fractions. How you simplify them, multiply, divide, add and subtract them.
When we talk about Algebraic fractions, we talk about having equations as numerators and denominators such as \(\frac{(x+1)}{(x-2)}\).
Simplifying Algebraic Fractions
The best way to go about simplifying fractions is to cancel out like terms on the top with like terms on the bottom.
This could be if you have an $x$ on top, you can cancel out an \(x\) on the bottom. However, it’s really important to understand that if there is a \(+\) or a \(-\), the \(x\) will need to be taken from both sides of the operator.
That sounds a bit confusing written down but let me show you an example.
First lets have a look at one without a \(+\) or \(-\):
\(\frac{2x^2}{2x}\) – here we can cancel out 2 from both the top and the bottom to give us \(\frac{x^2}{x}\).
We can also cancel out \(x\)
\(\frac{x+xy}{x}\) —> now, here we’ve got a numerator that includes an \(x\) on both sides of \(+\) operator so we can cancel out the \(x\)’s leaving us with \(\frac{1+y}{1}\) or just \(1+y\).
Multiplying/Dividing Algebraic Fractions
Multiplying and dividing Algebraic fractions is the exact same as multiplying and dividing normal fractions.
For multiplying, you can just multiply across – so just multiply the numerators together and the denominators together and collect your terms.
For dividing, you simply flip either fraction then multiply it across.
Adding/Subtracting Algebraic Fractions
Similar to the above, adding and subtracting Algebraic fractions is the same as adding and subtracting any normal looking fractions.
The difference is, as we are dealing with unknowns, denominators and numerators can often look really ugly and confusing. The key here is to try and factorise these down into as simple a form as possible. Quite a few questions will also try to give you similar expressions on top and bottom (i.e. they may share a bracket that is the same) so that you can cancel them out to express the final answer in a simpler form.
Hopefully this all made sense. If you have any questions on this, please leave them in the comments below and I’ll get back to you as soon as possible.
If you’re happy with this, please go ahead and give the practice questions a go and ask any questions as you need.