Express 2(x-1)/(x^2-2x-3) - 1/(x-3) as a fraction in its simplest form.

The answer is 1/(x+1)I began by factorising the denominator of the first fraction:2(x-1)/(x^2-2x-3) - 1/(x-3) = 2(x-1)/(x-3)(x+1) - 1/(x-3) Next, I multiplied both the numerator and the denominator of the second fraction by (x+1) to get a common denominator:2(x-1)/(x-3)(x+1) - 1/(x-3) = 2(x-1)/(x-3)(x+1) - (x+1)/(x-3)(x+1) With this common denominator, I could then expand the brackets on the numerators and add/subtract accordingly:2(x-1)/(x-3)(x+1) - (x+1)/(x-3)(x+1) = (2x-2-x-1)/(x-3)(x+1) = (x-3)/(x-3)(x+1) The last step I did was dividing the common factor of (x-3) from the numerator and denominator to give:(x-3)/(x-3)(x+1) = 1/(x+1)