Question

$\frac{7}{x-1} = \frac{6x+1}{x+1} - \frac{3(1+2x^2)}{x^2-1}$

Resolva em IR, a equação acima.

Answer 1

vamos lá...

$\frac{7}{x-1} = \frac{6x+1}{x+1} - \frac{3(1+2x^2}{x^2-1} \\ \\ mmc=(x+1)(x-1) \\ \\ 7(x+1)=(6x+1)(x-1)-3(1+2x^2) \\ \\ 7x+7=\not6x^2-6x+x-1-3-\not6x^2 \\ \\ 7x+7=-6x+x-1-3 \\ \\ 7x+7=-5x-4 \\ \\ 7x+5x=-4-7 \\ \\ 12x=-11 \\ \\ x=- \frac{11}{12} \\ \\ S=\{- \frac{11}{12} \}$