Question

2x+1 sobre x-3 + 2 sobre x ao quadrado -9 igual a 1 (equacao fracionaria que recaem no segundo grau)

Answer 1

.
$\frac{2x+1}{x-3} + \frac{2}{x^2-9} =1 \\ \\ \frac{2x+1}{x-3} + \frac{2}{(x+3)(x-3)} =1 \\ \\ mmc=(x+3)(x-3)$

$(2x+1)(x+3)+2=(x+3)(x-3) \\ \\ 2x^2+6x+x+3+2=x^2-9 \\ \\ 2x^2+7x+5-x^2+9-0$

$x^{2} +7x+14=0 \\ \\ a=1 \\ b=7 \\ c=14$

$\Delta=b^2-4ac \\ \Delta=7^2-4(1)(14) \\ \Delta=49-56 \\ \Delta=-7$

$x= \frac{-b\pm \sqrt{\Delta} }{2a} = \frac{-7\pm \sqrt{-7} }{2} \\ \\ x'= \frac{-7+ \sqrt{-7} }{2} \\ \\ x"= \frac{-7- \sqrt{-7} }{2}$