作业帮分式计算题
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分式计算题
分式计算题
分式计算题
【参考答案】(2x²+10x+14)/(x+1)(x+2)(x+3)(x+4)
原式=[1/(1+x)]-[1/(x+2)]+[1/(x+4)]-[1/(x+3)]
=[(x+2)/(x+1)(x+2)]-[(x+1)/(x+1)(x+2)]
+[(x+3)/(x+3)(x+4)]-[(x+4)/(x+3)(x+4)]
=[(x+2-x-1)/(x+1)(x+2)]-[(x+3-x-4)/(x+3)(x+4)]
=[1/(x+1)(x+2)]+[1/(x+3)(x+4)]
=[(x+3)(x+4)/(x+1)(x+2)(x+3)(x+4)]+[(x+1)(x+2)/(x+1)(x+2)(x+3)(x+4)]
=[[x²+7x+12+x²+3x+2)/(x+1)(x+2)(x+3)(x+4)]
=(2x²+10x+14)/(x+1)(x+2)(x+3)(x+4)
=1/[(x+1)(x+2)]-1/[(x+3)(x+4)]
=(4x+10)/[(x+1)(x+2)(x+3)(x+4)]
=1/(x+1)+1/(x+4)-[1/(x+2)+1/(x+3)]
=(2x+5)/(x^2+5x+4)-(2x+5)/(x^2+5x+6)
=(2x+5)*2/[(x+1)(x+2)(x+3)(x+4)]