Video Transcript
Simplify four over 𝑥 plus three
plus two over 𝑥 minus two. Well it looks a little bit more
complicated, but the process we’re gonna follow is exactly the same as what we’ve
just been doing. Now the one thing that I would
recommend is putting brackets around your denominators, cause that’s gonna make life
a little bit easier as we go through here and make sure we don’t make any
mistakes. So we’re gonna take our first
denominator and multiply the top and the bottom of the other fraction by that
value. And we’ll take the second
denominator and multiply the top and the bottom of the first fraction by that
value. So the principle still sticks, 𝑥
minus two divided by 𝑥 minus two is just one. So we’ve still got one times the
first fraction, so it’s still the first fraction. And 𝑥 plus three divided by 𝑥
plus three is still one. So we’ve got one times the second
fraction. So it’s still just two over 𝑥
minus two. Okay let’s multiply those out. Well we combine them into one
fraction here. We’ve got four lots of 𝑥 minus two
plus two lots of 𝑥 plus three all over the common denominator of 𝑥 minus two times
𝑥 plus three. So now we’re going to do four lots
of 𝑥 and four lots of negative two and we’re gonna add two lots of 𝑥 and two lots
of positive three. So four lots of 𝑥 is four 𝑥 and
four lots of negative two is negative eight. Two lots of 𝑥 is positive two 𝑥
and two lots of three is positive six. Now I’m not multiplying out the
denominator at this stage, because we’re not finished tidying up the numerator. Who knows? Things might factorise and
something might cancel out. If I multiply the denominator out,
I wouldn’t be able to spot that.
Well four 𝑥 plus two 𝑥 is six 𝑥
and negative eight plus six is negative two. So we’ve got six 𝑥 minus two over
𝑥 minus two times 𝑥 plus three. But in fact, if we look carefully
at the numerator, we can see that that will factorise. Six and two got common factor of
two. So what do I have to multiply two
by to get six 𝑥? Well that would be three 𝑥. And what do I have to multiply two
by to get negative two? Well that would be minus one. So there we go. Now what we’ve ended up with inside
the bracket isn’t the same as any of the brackets of the bottom. So nothing is gonna cancel, but
this is a nice factored format of our answer. Now if I had multiplied out the
denominator and I hadn’t factored the numerator, that’s the solution I would have
got and still be a perfectly correct answer. But people tend to leave it in this
factored format rather than this multiplied out format.
