MatemáticasBásico1 respuestas

1 / (a - b)(a - c) + 1 / (b - c)(b - a) + 1 / (c - b)?

1 / (a - b)(a - c) + 1 / (b - c)(b - a) + 1 / (c - b).

En resumen

<img src="https://tex.z-dn.net/?

Mejor respuesta

Lepud
8

ResolucióN

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%7D%2B%5Cfrac%7B1%7D%7B%5Cleft%28b-c%5Cright%29%5Cleft%28b-a%5Cright%29%7D%2B%5Cfrac%7B1%7D%7B%5Cleft%28c-b%5Cright%29%7D" />

Encontrar el mínimo común denominador para :

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%7D%2B%5Cfrac%7B1%7D%7B%5Cleft%28b-c%5Cright%29%5Cleft%28b-a%5Cright%29%7D%2B%5Cfrac%7B1%7D%7Bc-b%7D%3A%5Cquad%20%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29" />

Reescribir las fracciones :

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%5Ccdot%20%5Cleft%28b-c%5Cright%29%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D-%5Cfrac%7B1%5Ccdot%20%5Cleft%28a-c%5Cright%29%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D-%5Cfrac%7B1%5Ccdot%20%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D" />

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%5Ccdot%20%5Cleft%28b-c%5Cright%29-1%5Ccdot%20%5Cleft%28a-c%5Cright%29-1%5Ccdot%20%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D" />

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7Bb-c-%5Cleft%28a-c%5Cright%29-%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D" />

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7B-a%5E2-a%2Bac%2Bab%2Bb-bc%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D" />

Respuesta

<img src="https://tex.z-dn.net/?f=%0A%5Cboxed%7B%5Cboxed%7B%5Cfrac%7B-a%5E2-a%2Bac%2Bab%2Bb-bc%7D%7B%5Cleft%28a-b%5Cright%29%5Cleft%28a-c%5Cright%29%5Cleft%28b-c%5Cright%29%7D%7D%7D%7D%7D" />.