1) 4x^2 + x - 3/x^2 -1 = 4x^2 + 4x - 3x - 3/(x-1)(x+1) = 4x(x+1) - 3(x+1)/(x-1)(x+1) = (x +1)(4x - 3)/(x -1)(x + 1) = 4x - 3/x - 1
2) 2y^2 + 3y - 5/ y^2 + 5y -2y - 5/(y - 1)^2 = y(2y+5) - (2y+5)/(y - 1)^2 = (2y+5)(y-1)/(y-1)^2 = 2y+5/y - 1
3) a^2 + 5a + 4/a^2 - a - 20 = a^2 + 4a + a +4/a^2 + 4a - 5a - 20 = a(a + 4) + a + 4/a(a + 4) - 5(a + 4) = (a + 4)(a + 1)/(a + 4)(a - 5) = a + 1/ a - 5
4) 3 + 20b -7b^2/7b^2 - 6b - 1 = -7b^2 + 20b + 3/7b^2 - 7