8/x-8+11/x-11=9/x-9+10/x-10 ( giải phương trình )

0 bình luận về “8/x-8+11/x-11=9/x-9+10/x-10 ( giải phương trình )”

1. `\qquad 8/{x-8}+{11}/{x-11}=9/{x-9}+{10}/{x-10}` $(1)$

   `ĐK:x\ne 8;9;10;11`

   `(1)<=>(8/{x-8}+1)+({11}/{x-11}+1)=(9/{x-9}+1)+({10}/{x-10}+1)`

   `<=>{8+x-8}/{x-8}+{11+x-11}/{x-11}={9+x-9}/{x-9}+{10+x-10}/{x-10}`

   `<=>x/{x-8}+x/{x-11}=x/{x-9}+x/{x-10}`

   `<=>x/{x-8}+x/{x-11}-x/{x-9}-x/{x-10}=0`

   `<=>x(1/{x-8}+1/{x-11}-1/{x-9}-1/{x-10})=0`

   `<=>`$\left[\begin{array}{l}x=0(T M)\\\dfrac{1}{x-8}+\dfrac{1}{x-11}-\dfrac{1}{x-9}-\dfrac{1}{x-10}=0\ (2)\end{array}\right.$

   $\\$

   `(2)<=>1/{x-8}+1/{x-11}-1/{x-9}-1/{x-10}=0`

   `<=>1/{x-8}+1/{x-11}=1/{x-9}+1/{x-10}`

   `<=>{x-11+x-8}/{(x-8)(x-11)}={x-10+x-9}/{(x-10)(x-9)}`

   `<=>{2x-19}/{x^2-11x-8x+88}={2x-19}/{x^2-10x-9x+90}`

   `<=>{2x-19}/{x^2-19x+88}-{2x-19}/{x^2-19x+90}=0`

   `<=>(2x-19)(1/{x^2-19x+88}-1/{x^2-19x+90})=0` (*)

   Vì `x^2-19+88\ne x^2-19x+90`

   `=>1/{x^2-19x+88}-1/{x^2-19x+90}\ne 0`

   (*)`=>2x-19=0`

   `<=>x={19}/2(T M)`

   Vậy tập nghiệm của phương trình là:

   `S={0;{19}/2}`

   Trả lời