Thực hiện phép tính $\frac{x^2}{(x – y)(x – z)}$ + $\frac{y^2}{(y – x)(y – z)}$ + $\frac{z^2}{(z – x)(z – y)}$ Mình cảm ơn

0 bình luận về “Thực hiện phép tính $\frac{x^2}{(x – y)(x – z)}$ + $\frac{y^2}{(y – x)(y – z)}$ + $\frac{z^2}{(z – x)(z – y)}$ Mình cảm ơn”

1. ` (x^2)/((x-y)(x-z)) + (y^2)/((y-x)(y-z)) + (z^2)/((z-x)(z-y))`

   ` = (x^2)/((x-y)(x-z)) – (y^2)/((x-y)(y-z)) + (z^2)/((x-z)(y-z))`

   ` = (x^2*(y-z))/((x-y)(y-z)(x-z)) – (y^2*(x-z))/((x-y)(y-z)(x-z))  + (z^2 * (x-y))/((x-y)(y-z)(x-z))`

   ` = (x^2*(y-z) – y^2(x-z) + z^2(x-y))/((x-y)(y-z)(x-z))`

   ` = (x^2y – x^2z – y^2x + y^2z + z^2x – z^2y)/((x-y)(y-z)(x-z))`

   ` = (y(x^2-z^2)-y^2(x-z) – xz(x-z))/((x-y)(y-z)(x-z))`

   ` = ((x-z)[y(x+z) – y^2 – xz])/((x-y)(y-z)(x-z))`

   ` = (xy + yz  -y^2-xz)/((x-y)(y-z))` 

   ` = (y(x-y) – z(x-y))/((x-y)(y-z))` 

   ` = ((y-z)(x-y))/((x-y)(y-z))`

   ` = 1`

   Vậy giá trị của biểu thức bằng `1`

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