# Make y the subject of (y/x)+(2y/(x+4))=3

We want to make y the subject of the equation and so we need to write it in the form y=f(x) where f(x) is a function in terms of x.

When rearranging equations with fractions for a certain subject, factorising will usually be involved. A good start to this would be to put everything over a common denominator (x(x+4)) which is the product of the two different denominators in the original equation. Recall that to maintain **equality** (i.e. the left hand side equals the right hand side), **what you do to one side you must also do to the other side. **This is an incredibly important rule that will help you solve the **majority, if not, all** of maths problems you will come across while avoiding mistakes.

So, to (y/x), we multiply by (x+4)/(x+4). Note that this is equal to 1, as any number divided by itself is 1, and any number multipled by 1 is itself so we aren't actually changing the equation. Simlarly for (2y/(x+4)) we multiply by (x/x). For the right hand side of the equation, we can multiply by (x(x+4))/(x(x+4)).

This gives us:

(y(x+4)+2xy)/(x(x+4))=3(x(x+4))/(x(x+4))

At this point we can multiply everything on both sides of the equation by (x(x+4)) to remove the denominator. We can do this because of the rule mentioned earlier: **what we do to one side of the equation we must also do to the other side of the equation.**

After this step we have:

xy+4y+2xy=3(x(x+4))

We want y as the subject of the equation so on the left hand side we factorise out the y term, as every term on the left hand side has y in it.

y(x+4+2x)=y(4+3x)=3(x(x+4))

Finally, we divide both sides by (4+3x):

y=(x(x+4))/(4+3x)