Question

Aduceti la forma cea mai simpla ecuatia :
 E(x)= (5 supra x-2 + 2 supra x+2-6 supra x²-4) : ( x²+4 supra X²-4  +1 in dreptul liniei de fractie )

Answer 1

$E(x)= (\frac{5}{x-2} + \frac{2}{x+2} - \frac{6}{ x^{2} -4} ): (\frac{ x^{2} +4}{ x^{2} -4} +1)= \\ =(\frac{5(x+2)}{(x-2)(x+2)} + \frac{2(x-2)}{(x+2)(x-2)} - \frac{6}{ x^{2} -4}): (\frac{ x^{2} +4}{ x^{2} -4} +\frac{ x^{2} -4}{ x^{2} -4})= \\ = \frac{5x+10+2x-4-6}{ x^{2} -4} : \frac{ x^{2} +4+ x^{2} -4}{ x^{2} -4} = \\ =\frac{7x}{ x^{2} -4} : \frac{ 2x^{2}}{ x^{2} -4} = \\ =\frac{7x}{ x^{2} -4}* \frac{{ x^{2} -4}}{{ 2x^{2}}}= \\ = \frac{7}{ 2x }$