Question

50 POINTS REWARD!!
please answer all of the following questions correctly:

Answer 1

`(3x-2)/(x^(2)-2x-3) -(1)/(x-3)`

factorising the first denominator

x²-2x-3 = x² -3x+x-3 = (x+1)(x-3)

(a)
`(3x-2)/((x+1)(x-3)) - (1)/(x-3)`

finding LCD

(b) LCD of (x-3)(x+1) and (x-3) is (x-3)(x+1)

(c)

`(3x-2)/((x-3)(x+1)) -(x+1)/((x-3)(x+1))`

(d)

`(3x-2-(x+1))/((x-3)(x+1))`

`(3x-2-x-1)/((x-3)(x+1))`

`(2x-3)/((x-3)(x+1))`