Question

As soluçoes da equaçao x-a/x+a + x+a/x-a= 2.(a4+1) / a²(x²-a²) , onde a ≠ 0, são:

Answer 1

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$\frac{x-a}{x+a} + \frac{x+a}{x-a} = \frac{2(a^4+1)}{a^2(x^2-a^2)}$

mmc=a^²(x²-a²)

$a^2(x-a)(x-a)+a^2(x+a)(x+a)=2(a^4+1) \\ \\ a^2(x^2-2ax+a^2)+a^2(x^2+2ax+a^2)=2a^4+2 \\ \\ a^2x^2-2a^3x+a^4+a^2x^2+2a^3x+a^4-2a^4=2 \\ \\ 2a^2x^2+2a^4-2a^4=2 \\ \\ 2a^2x^2=2 \\ \\ x^2= \frac{2}{2a^2} \\ \\ x^{2}= \frac{1}{a^2} \\ \\ x= \sqrt{ \frac{1}{a^2} } =\pm \frac{1}{a}$