1) cộng các phân thức đại số
b) (x - 15)/(x - 3) + 18(x - 2)/(x^2 - 6x + 9)
= (x - 15)(x - 3)/(x - 3)^2 + 18(x - 2) / (x - 3)^2
= [ (x - 15)(x - 3) + 18(x - 2)] / (x - 3)^2
= (x^2 - 3x - 15x + 45 + 18x - 36)/(x - 3)^2
= (x^2 + 9) / (x - 3)^2

1) cộng các phân thức đại số
c) (1 - 3x)/2x + (3x - 2)/(2x - 1) + (3x - 2)/(2x - 4x^2)
= (1 - 3x)(1 - 2x) / 2x(1 - 2x) - (3x - 2)2x/(1 - 2x)2x + (3 - 2x)/2x(1 - 2x)
= [ (1 - 3x)(1 - 2x) - (3x - 2)*2x + (3 - 2x)] / 2x(1 - 2x)
= (1 - 2x - 3x + 6x^2 - 6x^2 + 4x + 3 - 2x) / 2x(1 - 2x)
= (-3x + 4)/2x(1 - 2x)

1) cộng các phân thức đại số
d) (4 - x^2)/(x - 3) + (2x - 2x^2)/(3 - x) + (5 - 4x)/(x - 3)
= (4 - x^2)/(x - 3) - (2x - 2x^2)/(x - 3) + (5 - 4x)/(x - 3)
= [ (4 - x^2) - (2x - 2x^2) + (5 - 4x) ] / (x - 3)
= (4 - x^2 - 2x + 2x^2 + 5 - 4x) / (x - 3)
= (x^2 - 6x + 9) / (x - 3)
= (x - 3)^2 / (x - 3)
= x - 3

1) cộng các phân thức đại số
f) x/(x + 2) + 4x/(x^2 - 4) - x/(2 - x)
= x(x - 2)/(x + 2)(x - 2) + 4x/(x - 2)(x + 2) + x(x + 2)/(x - 2)(x + 2)
= [ x(x - 2) + 4x + x(x + 2)] / (x - 2)(x + 2)
= (x^2 - 2x + 4x + x^2 + 2x) / (x - 2)(x + 2)
= (2x^2 + 4x) / (x - 2)(x + 2)
= 2x(x + 2)/(x - 2)(x + 2)
= 2x/(x - 2)

a) x^2/2x+6 + 6x+9/2x+6 = (x^2 + 6x + 9)/2x+6 = (x+3)^2/2(x+3) = x+3/2
b)x-15/x-3 + 18(x-2)/x^2-6x+9
= x-15/x-3 + 18(x-2)/(x-3)^2
= (x-15)(x-3)/(x-3)^2 + 18(x-2)/(x-3)^2
= (x-15)(x-3) + 18(x-2) / (x-3)^2
= ( x^2 - 15x - 3x + 45 + 18x - 36 ) / (x-3)^2
= x^2 + 9/(x-3)^2
c)1-3x/2x + 3x-2/2x-1 + 3x-2/2x-4x^2
= (1-3x)(2x-1) / 2x(2x-1) + (3x-2).2x/2x(2x-1) - 3x-2/4x^2 - 2x
= 1 - 6x^2 - 1 + 3x / 4x^2 - 2x + 6x^2 - 4x/4x^2 - 2x - 3x-2/4x^2 - 2x
= -6x^2 + 3x/4x^2 - 2x + 6x^2 - 4x/4x^2 - 2x - 3x-2/4x^2 - 2x
= -6x^2 + 3x + 6x^2 - 4x - 3x + 2 / 4x^2 - 2x
= -4x + 2/4x^2 - 2x
= -2(2x-1)/2x(2x-1)
= -1/x
d) 4-x^2/x-3 + 2x-2x^2/3-x + 5-4x/x-3
= 4-x^2/x-3 - 2x - 2x^2/x-3 + 5-4x/x-3
= 4-x^2 - 2x + 2x^2 + 5 - 4x / x - 3
= x^2 - 6x + 9 / x - 3
= ( x - 3 )^2 / x - 3
= x - 3
e)4x^2-3x+17/x^3-1 + 2x-1/x^2+x+1 + 6/1-x
= 4x^2 - 3x + 17/x^3 - 1 + (2x-1)(x-1) / x^3 - 1 - 6/x-1
= 4x^2 - 3x + 17/x^3 - 1 + 2x^2 - x - 2x + 1 / x^3 - 1 - 6(x^2 + x + 1)/x^3 - 1
= 4x^2 - 3x + 17/x^3 - 1 + 2x^2 - 3x + 1/x^3 - 1 - 6x^2 + 6x + 6 / x^3 - 1
= 4x^2 - 3x + 17 + 2x^2 - 3x + 1 - 6x^2 - 6x - 6 / x^3 - 1
= -12x + 12 / x^3 - 1
= -12(x-1) / (x-1)(x^2 + x + 1)
= -12/x^2 + x + 1
f)x/x+2 + 4x/x^2-4 - x/2-x
= x(x-2) / x^2 - 4 + 4x/x^2 - 4 + x/x-2
= x^2 - 2x/x^2 - 4 + 4x/x^2 - 4 + x(x+2) / x^2 - 4
= x^2 - 2x/x^2 - 4 + 4x/x^2 - 4 + x^2 + 2x/x^2 - 4
= x^2 - 2x + 4x + x^2 + 2x / x^2 - 4
= 2x^2 / x^2 - 4

Sửa lại f)
= 2x^2 + 4x / x^2 - 4
= 2x(x+2) / (x+2)(x-2)
= 2x/x-2