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4/(x+3) -5/(x-1)
(4(x-1) - 5(x+3))/(x+3)(x-1)
(4x-4 -5x-3)/(x+3)(x-1)
(-x-7)/(X+3)(x-1)
(-x-7)/x^2+2x-3

4/(x+3) - 5/(x-1)
= 4(x-1)-5(x+3) / (x^2+2x-3)
= 4x-4-5x-15 / (x^2+2x-3)
= -x-19 / (x^2+2x-3)