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计算：(1)/(x-3)÷(x+2)/(x^2-9)-(1)/(x^2+5x+6)

分类: 作业答案 • 2021-12-28 11:15:11
问题描述：

计算：(1)/(x-3)÷(x+2)/(x^2-9)-(1)/(x^2+5x+6)

答

1/(x-3)÷(x+2)/(x^2-9)-1/(x^2+5x+6)
=1/(x-3)÷(x+2)/[(x-3)(x+3)]-1/(x+2)(x+3)
=1/(x-3)*(x-3)(x+3)/(x+2)-1/(x+2)(x+3)
=(x+3)/(x+2)-[1/(x+2)-1/(x+3)]
=(x+3)/(x+2)-1/(x+2)+1/(x+3)
=(x+3-1)/(x+2)+1/(x+3)
=1+1/(x+3)
=(x+3+1)/(x+3)
=(x+4)/(x+3)

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