Question

Resolva a equação:
x²/x-3 -x+6/x-3=1

Answer 1

Resposta:

Explicação passo-a-passo:

$\displaystyle \frac{x^{2}}{x-3} -\frac{x+6}{x-3} =1\\\\x^{2}-(x+6)=x-3\\x^{2}-x-6=x-3\\x^2}-2x-3=0\\\\\displaystyle~Aplicando~a~f\'{o}rmula~de~Bhaskara~para~x^{2}-2x-3=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=1{;}~b=-2~e~c=-3\\\\\Delta=(b)^{2}-4(a)(c)=(-2)^{2}-4(1)(-3)=4-(-12)=16\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(-2)-\sqrt{16}}{2(1)}=\frac{2-4}{2}=\frac{-2}{2}=-1\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(-2)+\sqrt{16}}{2(1)}=\frac{2+4}{2}=\frac{6}{2}=3\\\\S=\{-1,~3\}$

Answer 2

Resposta:

x = - 9/2

Explicação passo-a-passo:

x²/x - 3 - x + 6/x - 3 = 1

x² - x(x - 3) + 6/x - 3 = 1

x² - x² + 3x + 6/x - 3 = 1

3x + 6/x - 3 = 1 (× por x - 3)

3x + 6 = x - 3

3x - x = - 3 - 6

2x = - 9

x = - 9/2

Espero ter ajudado.