作业帮当x=9/2时,求(x^2+7x+10)/(x^2+6x+5)×(x^3+1)/(x^2+4x+4)÷(x^2-x+1)
来源：学生作业帮 编辑：拍题作业网作业帮 分类：数学作业 时间：2024/04/28 21:22:46
当x=9/2时,求(x^2+7x+10)/(x^2+6x+5)×(x^3+1)/(x^2+4x+4)÷(x^2-x+1)/(x+2)
(x^2+7x+10)/(x^2+6x+5)×(x^3+1)/(x^2+4x+4)÷(x^2-x+1)/(x+2)
=(x+2)(x+5)/(x+1)(x+5)*(x+1)(x^2-x+1)/(x+2)^2÷(x^2-x+1)/(x+2)
=(x+2)(x+5)/(x+1)(x+5) * (x+1)(x^2-x+1)/(x+2)^2 * (x+2)/(x^2-x+1)
=1
再问： (x+1)(x^2-x+1)/(x+2)^2是怎么来的？我不懂！谢谢了！
再答： x^3+1=(x+1)(x^2-x+1) 依据：立方和公式，a^3+b^3=(a+b)(a^2-ab+b^2) x^2+4x+4=(x+2)^2即(x+2)² 依据：完全平方公式，(a+b)^2=a^2+2ab+b^2逆用
=(x+2)(x+5)/(x+1)(x+5)*(x+1)(x^2-x+1)/(x+2)^2÷(x^2-x+1)/(x+2)
=(x+2)(x+5)/(x+1)(x+5) * (x+1)(x^2-x+1)/(x+2)^2 * (x+2)/(x^2-x+1)
=1
再问： (x+1)(x^2-x+1)/(x+2)^2是怎么来的？我不懂！谢谢了！
再答： x^3+1=(x+1)(x^2-x+1) 依据：立方和公式，a^3+b^3=(a+b)(a^2-ab+b^2) x^2+4x+4=(x+2)^2即(x+2)² 依据：完全平方公式，(a+b)^2=a^2+2ab+b^2逆用
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