Make x the subject

[Pat_1211]

I'm doing a past GCSE paper at the moment and struggling with this question.

Make x the subject

ax+by
_____ = 3d
x-y

How do u do it.

[Saucerer]

(ax+by)/(x-y)=3d

so ax+by = 3d(ax+by)

expand the brackets

ax+by = 3adx+3bdy

Take the x terms to the left hand side

ax-3adx = 3bdy-by
factorise the left hand side
x(a-3ad)=by(3d-1)
so
x=by(3d-1)/(a-3ad)