化简:[√(x^2-6x+9)/x^2-x-12]*(x^3-16x)/(x^2-3x)-1/(x+3) {x>3}
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:2024/04/27 19:30:14
化简:[√(x^2-6x+9)/x^2-x-12]*(x^3-16x)/(x^2-3x)-1/(x+3) {x>3}
分步写,好让看的清楚符号
[√(x^2-6x+9)/x^2-x-12]=√(x-3)^2 /(x-4)(x+3)=(x-3)/(x-4)(x+3);
(x^3-16x)/(x^2-3x)=x(x^2-16)/x(x-3)=(x+4)(x-4)/(x-3);
原式=(x-3)/(x-4)(x+3)* (x+4)(x-4)/(x-3)-1/(x+3)=(x+4)/(x+3)-1/(x+3)=1
[√(x^2-6x+9)/x^2-x-12]=√(x-3)^2 /(x-4)(x+3)=(x-3)/(x-4)(x+3);
(x^3-16x)/(x^2-3x)=x(x^2-16)/x(x-3)=(x+4)(x-4)/(x-3);
原式=(x-3)/(x-4)(x+3)* (x+4)(x-4)/(x-3)-1/(x+3)=(x+4)/(x+3)-1/(x+3)=1
化简:[√(x^2-6x+9)/x^2-x-12]*(x^3-16x)/(x^2-3x)-1/(x+3) {x>3}
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