Simple maths question...

work out (5 over (x-2)) + (2 over (2-x))
its easier if u ryt it down
the answer is 3 over (x-2) but id like to see the steps plz and thank you!

imagine you wanted to add 2/3 and 2/8
You would find a common denominator which could be 3 times 8 = 24
you then have to change 2/3 into something over 24 Well you multiply the denominator by 8
So 2/3 = 16/24 and 2/8 = 6/24
Same principle applies here
Make ypur denominator be (x - 2)(2 - x)
so multiply 5 by (2 - x) and 2 by (x - 2)
your problem is now [ 5(2 - x) + 2(x - 2)] / [ (x - 2)(2 - x)
= [10 - 5x + 2x - 4] / (x - 2)(2 - x) I am not expanding bottom line just yet to see what happens
= [6 - 3x] / (x - 2)(2 - x) Now look at the top line there is a factor 0f 3 in it
= [3(2-x)] / (x - 2)(2 - x) (2-x) divided by (2 - x) = 1 so this can cancel on both lines
= 3/(x-2)
Try it out putting a number in for x just to prove to yourself that it is right

Remember that x - 2 = -(2 - x)

5/(x - 2) + 2/(2 - x) = 5/(x - 2) - 2/(x - 2)

5/(x - 2) + 2/(2 - x) = 3/(x - 2)