Question

Dada a função F(x)=x/x+1 - 1/2x-3,calcule x de modo que f(x)=-1/3.Obs: Somente letra B.

Answer 1

$f(x) = \frac{x}{x+1} - \frac{1}{2x-3} \\ \\ \frac{-1}{3} = \frac{x(2x-3) - 1.(x+1)}{(x+1)(2x-3)} \\ \\ \frac{-1}{3} = \frac{2x^2-3x - x - 1}{2x^2-3x+2x-3} \\ \\ -1(2x^2 - x - 3) = 3(2x^2 - 4x - 1) \\ \\ -2x^2 + x + 3 = 6x^2 - 12x - 3 \\ \\ 6x^2 + 2x^2 - 12x - x - 3 - 3 = 0 \\ 8x^2 - 13x - 6 = 0$

Δ = 361

x = -(-13) +- √361/2.8

x1 = 13 + 19/16 = 32/16 = 2
x2 = 13-19/16 = -6/16 = -3/8

x = 2