计算：(x²-2x-8)分之(2-x)+(3x+6)分之(x+4)

计算：(x²-2x-8)分之(2-x)+(3x+6)分之(x+4)
计算：(x²-2x-8)分之(2-x)+(3x+6)分之(x+4)

计算：(x²-2x-8)分之(2-x)+(3x+6)分之(x+4)
解
原式
=3(2-x)/3(x-4)(x+2)+(x+4)(x-4)/3(x+2)(x-4)
=(6-3x)/3(x-4)(x+2)+(x²-16)/3(x+2)(x-4)
=(6-3x+x²-16)/3(x+2)(x-4)
=(x²-3x-10)/3(x+2)(x-4)
=(x-5)(x+2)/3(x+2)(x-4)
=(x-5)/3(x-4)

(2-x)/(x²-2x-8)+(x+4)/(3x+6)
=(2-x)/[(x-4)(x+2)]+(x+4)/[3(x+2)]
=3(2-x)/[3(x-4)(x+2)+[(x+4)(x-4)]/[3(x-4)(x+2)]
=(6-3x+x²-16)/[3(x-4)(x+2)]
=(x²-3x-10)/[3(x-4)(x+2)]
=(x-5)(x+2)/[3(x-4)(x+2)]
=(x-5)/{3(x-4)]