Determine el valor de “x” ((x - a) ^ 2 + (x - a) ^ 2) / ((x - a)(x - b)) + 4ab / (a ^ 2 - b ^ 2 ) = 0?

<img src="https://tex.z-dn.net/?f=%5Cleft%28%5Cleft%28%5Cleft%28x-a%5Cright%29%5E2%2B%5Cleft%28x-a%5Cright%29%5E2%5Cright%29%2F%5Cleft%28%5Cleft%28x-a%5Cright%29%5Cleft%28x-b%5Cright%29%5Cright%29%5Cright%29%5C%3A%2B%5Cleft%28%5Cleft%284ab%5Cright%29%2F%5Cleft%28a%5E2-b%5E2%5C%3A%5Cright%29%5Cright%29%3D0" /> :

Resolvemos <img src="https://tex.z-dn.net/?f=%5Cleft%28%5Cleft%28%5Cleft%28x-a%5Cright%29%5E2%2B%5Cleft%28x-a%5Cright%29%5E2%5Cright%29%2F%5Cleft%28%5Cleft%28x-a%5Cright%29%5Cleft%28x-b%5Cright%29%5Cright%29%5Cright%29" />

Sumamos elementos similares

<img src="https://tex.z-dn.net/?f=%28x-a%5Cright%29%5E2%2B%5Cleft%28x-a%5Cright%29%5E2%3D2%5Cleft%28x-a%5Cright%29%5E2" />

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B2%5Cleft%28x-a%5Cright%29%5E2%7D%7B%5Cleft%28x-a%5Cright%29%5Cleft%28x-b%5Cright%29%7D" />

Eliminamos elemento común <img src="https://tex.z-dn.net/?f=%28x-a%29" /> :

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7B2%5Cleft%28x-a%5Cright%29%7D%7Bx-b%7D" />

Sustituimos :

<img src="https://tex.z-dn.net/?f=2%28x-a%29%20%3D%20%282x%20-%202a%29" />

<img src="https://tex.z-dn.net/?f=%3D%5Cfrac%7B2x-2a%7D%7Bx-b%7D%2B%5Cfrac%7B4ab%7D%7Ba%5E2-b%5E2%7D" />

Encontramos el mínimo común denominador para <img src="https://tex.z-dn.net/?f=%5Cfrac%7B2x-2a%7D%7Bx-b%7D%2B%5Cfrac%7B4ab%7D%7Ba%5E2-b%5E2%7D%3A%5Cquad%20%5Cleft%28x-b%5Cright%29%5Cleft%28a%5E2-b%5E2%5Cright%29" />

Reescribimos basados en el mínimo común denominador : = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Cleft%282x-2a%5Cright%29%5Cleft%28a%5E2-b%5E2%5Cright%29%7D%7B%5Cleft%28x-b%5Cright%29%5Cleft%28a%5E2-b%5E2%5Cright%29%7D%2B%5Cfrac%7B4ab%5Cleft%28x-b%5Cright%29%7D%7B%5Cleft%28x-b%5Cright%29%5Cleft%28a%5E2-b%5E2%5Cright%29%7D" /> = [img = 10]

Resolvemos [img = 11] = [img = 12]

Resolvemos [img = 13]

[img = 14]

Tenemos [img = 15]

Sabemos que [img = 16]

Entonces :

[img = 17]

Restamos [img = 18] de ambos lados :

[img = 19][img = 20]

Simplificamos :

[img = 21]

Factorizamos [img = 22]

[img = 23]

Dividimos ambos lados entre [img = 24]

[img = 25]

Finalmente simplificamos :

[img = 26].