Question

Resolva as seguintes equações literais na variável x:

B) x-a/(a+1) - x+a/(a-1) + 2/(a^2 -1)

C) mx-m/(x^2 -2x+1) + nx+n/(x^2-1) = 1/2

Me ajude pfvvv

Answer 1

Olá!

Questão b)

$\dfrac{x-a}{a+1}~-~\dfrac{x+a}{a-1}~+~\dfrac{2}{a^{2}-1 }~=~0 \\ \\ \\\\ \dfrac{x-a}{a+1}~-~\dfrac{x+a}{a-1}~+~\dfrac{2}{(a+1)*(a-1) }~=~0\\ \\ \\ \\ \dfrac{[(a-1)*(x-a)]~-~[(a+1)*(x+a)]~+~2}{(a+1)*(a-1)} ~=~0\\ \\ \\ \\ \left[(a-1)*(x-a)\right]~-~[(a+1)*(x+a)]~+~2~=0*(a+1)*(a-1)\\ \\ \\ \left[(a-1)*(x-a)\right]~-~[(a+1)*(x+a)]~+~2~=0\\ \\ \\ (ax-a^{2}-x+a)~-~(ax+a^{2}+x+a )+2=0\\ \\ \\ ax-a^{2}-x+a-ax-a^{2}-x-a +2~=~0\\ \\ \\ -2a^{2}-2x+2=0~~~~~~~\div(-2)\\ \\ a^{2} +x-1=0$

$\boxed{x=1-a^{2}~~~~~com~~~~ a\neq -1,~~ \neq1 }$

Questão c)

$\dfrac{mx-m}{x^{2}-2x+1 } ~+~\dfrac{nx+n}{x^{2} -1} ~=~\dfrac{1}{2} \\ \\ \\ \\ \dfrac{m*(x-1)}{(x-1)*(x-1) } ~+~\dfrac{n*(x+1)}{(x+1)*(x-1} ~=~\dfrac{1}{2}\\ \\ \\ \\ \dfrac{m}{(x-1) } ~+~\dfrac{n}{(x-1)} ~=~\dfrac{1}{2}\\ \\ \\ \\ \dfrac{2m+2n}{2*(x-1)}~=~x-1\\ \\ \\ \\ 2m+2n=x-1\\ \\ \\\\ \boxed{x=2m+2n+1}$

:)