x/(2x-3) + 4/(x+1) =1 [5 mark question]

We have 2 fractions we want to get rid off to make it easier, so what we do is multiply both sides by the things we want to get rid off.In this case we multiply both sides by (2x-3)(x+1)This gives us x(x+1) + 4(2x-3) = 1(2x-3)(x+1)now we expand the bracketsx² + x + 8x - 12 = 2x² -x -3now we collect all the terms (i.e - put all x ,x² and constants in one group)0= x² -10x + 9factorise this by finding 2 numbers which add to -10 and times to make 9this is -9 and -1this means x²-10x + 9 = (x-9)(x-1) = 0 one of the brackets has to equal 0, so x = 9 or x = 1