Math Help: How To Change The Subject-

Uploaded by vividmaths on 14.03.2012

Ok, guys here’s our chance to do a really challenging question. What we are going to
do here is make “a” the subject of this formula. At the present moment as you can
see “b” is the subject so how we make “a” the subject particularly when there
are two “a’s” on top here of “a” minus three (a-3) and again “a” minus
four (a-4) as the denominator.
So the first thing we have to do is multiply both sides by “a” minus four (a-4) or
if you want to think of it as cross multiplying that corner times that corner it’s still
the same process. So let’s multiply both sides by “a” minus four (a-4). “a”
minus four (a-4) and times “a” minus four (x a-4). Ok that will give here “b” outside
of a minus four equals (b (a-4=) and if we cancel this two guys, “a” minus four (a-4)
“a” minus four (a-4) which is simply left a minus three (a-3). Ok, let’s expand the
left hand side, so we have “b & a” minus four b equals "a" minus three (ba-4b=a-3).
Now what are we looking for, we are looking for getting the “a’s” together so what
I’m going to do is draw the 4b over the outside and “a” over this side. So, the
four b (+ 4b) will go to plus four b (+ 4b) and plus four b (+4b) here and at the same
time we are going to take away “a” and take away “a”, all right that’s an idea.
Alright, let’s do that now, so what we have here is “ba” minus “a” equals four
“b” minus three (ba-a=4b-3). Ok, let’s factor on the left hand side so we can make
“a” subject and we can take “a” out so it’s “a” bracket “b” minus one
equals four “b” minus three: a(b-1) = 4b-3. Ok, let’s divide both sides by “b” minus
one (b-1) and that will make this “a” the subject which is the outcome of this exercise
so let’s divide both sides by “b” minus one (b-1) so we'll divide it by “b” minus
one and “b” minus one (b-1) and if we write it up here it will become “a” equals;
and on the top we have four “b” minus three (4b-3)– all over and the “b” minus
one (b-1) over here and that is here is our answer: a is the subject.
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