Question

Calcular el dominio de la función: M(x)= √3x-2 +√5-x

Answer 1

$\mathrm{Desarrollar\:}M\left(x\right):\quad xM \\\\xM=\sqrt{3}x-2+\sqrt{5}-x \\\\\mathrm{Restar\:}\sqrt{3}x-x\mathrm{\:de\:ambos\:lados}\\\\xM-\left(\sqrt{3}x-x\right)=\sqrt{3}x-2+\sqrt{5}-x-\left(\sqrt{3}x-x\right)\\\\Simplificar\\\\xM-\sqrt{3}x+x=-2+\sqrt{5}\\\\\mathrm{Factorizar}\:xM-\sqrt{3}x+x:\quad x\left(M-\sqrt{3}+1\right)\\\\x\left(M-\sqrt{3}+1\right)=-2+\sqrt{5}\\\\\mathrm{Dividir\:ambos\:lados\:entre\:}M-\sqrt{3}+1;\quad \:M\ne \:-1+\sqrt{3}$

$\frac{x\left(M-\sqrt{3}+1\right)}{M-\sqrt{3}+1}=-\frac{2}{M-\sqrt{3}+1}+\frac{\sqrt{5}}{M-\sqrt{3}+1};\quad \:M\ne \:-1+\sqrt{3}\\\\Simplificar\\\\x=\frac{-2+\sqrt{5}}{M-\sqrt{3}+1};\quad \:M\ne \:-1+\sqrt{3}$

Saludos desde Colombia, espero que te sirva.