已知x^2 -2x-3=0 求[(x^2-3)/(x-1)-2]除以1/x-1
问题描述:
已知x^2 -2x-3=0 求[(x^2-3)/(x-1)-2]除以1/x-1
答
由x^2 -2x-3=0得:x=3或x=-1;
[(x^2-3)/(x-1)-2]÷[1/(x-1)]=[(x^2-3)/(x-1)-2](x-1)=x^2-3-2(x-1)=x^2-2x-1
当x=3时,x^2-2x-1=2;当x=-1时,x^2-2x-1=2,故:原式的值是2