Hard maths expression

simplify this as much as possible to be in its simplest form
7/(x-4)(X+3) - 4/(x+3)(x-1) it should turn out to be 3/(x-4)(x-1)

dont know how to get it or where to start

Multiply the left of the "-" by (x-1) / (x-1)
Multiply the right side of the "-" by (x-4) / (x-4)

7 (x-1) / (x-4)(x+3)(x-1) - 4 (x-4) / (x-4)(x+3)(x-1)

7x - 7 / SAME - 4x + 16 / SAME

7x - 7 - 4x + 16 / (x-4)(x+3)(x-1)
3x + 9 / (x-4)(x+3)(x-1)
3 (x+3) / (x-4)(x+3)(x-1)

The (X+3) / (X+3) cancels out giving you the answer:
3 / (x-4)(x-1)

Multiply the first term, up and down, by (x-1) and the second term, up and down, by (x-4)

7(x-1)/(x-4)(x+3)(x-1) - 4(x-4)/(x+3)((x-1)(x-4) now the denominators are the same... just add the numerators:

[7(x-1) -4(x-4)]/(x-4)(x+3)(x-1) ... now expand the numerator and collect the similar terms:

7x-7 -4x+ 16 = 3x+9 = 3(x+3) then we can simplify the factor (x+3) up and down

and get 3/(x-4)(x-1) OK!

First find a common denominator which would be (x-4)(x+3)(x-1), since it has to have all factors of both denominators.
Now multiply the first fraction by (x-1)/(x-1) and the second fraction by (x-4)/(x-4) so that you have a common denominator.
7(x-1)-4(x-4) is the new numerator

= (7x-7-4x+16)
------------------
(x-4)(x+3)(x-1)

=3x+9
------------
(x-4)(x+3)(x-1)

=3(x+3)
-------------------
(x-4)(x+3)(x-1)

Now cancel the x+3, and you have your answer!

7 / (x - 4) (x + 3) - 4 / (x + 3) (x - 1)

[Multiply up upon all of it (x + 3) to cancel the (x + 3) brackets]

7(x + 3) / (x - 4) (x + 3) - 4(x + 3) / (x + 3) (x - 1)

[This then cancels all the (x + 3) brackets in the equation leaving : ]

7 / (x - 4) - 4 / (x - 1)