Hallar el conjunto de verdad del predicado : r(x) : (√(x + 4) + √(x - 4)) / (√(x + 4) - √(x - 4)) = x - 3?

El conjunto de verdad es x = 4 o x = 5Tenemos la expresión : <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%20%2B%5Csqrt%7Bx-4%7D%20%7D%7B%5Csqrt%7Bx%2B4%7D%20-%5Csqrt%7Bx-4%7D%7D%20%3D%20x-3" />Multiplicamos y dividimos el lado izquierdo por el conjugado del denominador : <img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%2B%5Csqrt%7Bx-4%7D%7D%7B%5Csqrt%7Bx%2B4%7D%20-%5Csqrt%7Bx-4%7D%7D%2A%5Cfrac%7B%5Csqrt%7Bx%2B4%7D%20%2B%5Csqrt%7Bx-4%7D%7D%7B%5Csqrt%7Bx%2B4%7D%20%2B%5Csqrt%7Bx-4%7D%7D%3D%20x-3" />Multiplicando factores iguales y usando la propiedad (a - b) * (a + b) = a² - b²<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Csqrt%7Bx%2B4%7D%20%2B%5Csqrt%7Bx-4%7D%29%5E%7B2%7D%7D%7B%28%5Csqrt%7Bx%2B4%7D%29%5E%7B2%7D%20-%28%5Csqrt%7Bx-4%7D%29%5E%7B2%7D%7D%3D%20x-3" /><img src="https://tex.z-dn.net/?f=%5Cfrac%7B%28%5Csqrt%7Bx%2B4%7D%29%5E%7B2%7D%20%2B2%5Csqrt%7Bx%2B4%7D%5Csqrt%7Bx-4%7D%20%2B%28%5Csqrt%7Bx-4%7D%29%5E%7B2%7D%7D%7Bx%2B4%20-x%2B4%7D%3D%20x-3" /><img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B4%2B2%2A%5Csqrt%7B%28x%2B4%29%2A%28x-4%29%7D%20%2Bx-4%7D%7B8%7D%3D%20x-3" /><img src="https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B2%2A%5Csqrt%7B%28x%2B4%29%28x-4%29%7D%7D%7B8%7D%3D%20x-3" /><img src="https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B%5Csqrt%7B%28x%2B4%29%28x-4%29%7D%7D%7B4%7D%3D%20x-3" /><img src="https://tex.z-dn.net/?f=x%2B%5Csqrt%7B%28x%2B4%29%28x-4%29%7D%7D%3D%204x-12" /><img src="https://tex.z-dn.net/?f=%5Csqrt%7B%28x%2B4%29%28x-4%29%7D%7D%3D%203x-12" /><img src="https://tex.z-dn.net/?f=%28x%2B4%29%28x-4%29%3D%20%283x-12%29%5E%7B2%7D%20%3D%209x%5E%7B2%7D%20-72x%2B144" />[img = 10][img = 11]Si calculamos las raíces son : x = 4, y x = 5Entonces el conjunto de verdad es x = 4 o x = 5.