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

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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)

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