Question

Resolva as equações :
b) (3x+1)(x-1)-3(x+2)² = -9
Resp : -2/7

c) x-2/4 + 2x+8/5 = 5
Resp : 6

d) x+1/x-1 + 2x-5/x-3 =3
Resp : 7/3

Answer 1

$b) \\ \\ (3x + 1)(x - 1) - 3 *(x + 2)^2 = -9 \\ \\ 3x^2 - 3x + x - 1 - 3 *(x^2 + 4x + 4) + 9 = 0 \\ \\ 3x^2 - 2x - 1 - (3x^2 + 12x + 12) + 9 = 0 \\ \\ \not 3x^2 - 2x - 1 - \not 3x^2 - 12x - 12 + 9 = 0 \\ \\ -14x - 13 + 9 = 0 \\ \\ -14x - 4 = 0 (-1) \\ \\ 14x + 4 = 0 \\ \\ 14x = -4 \\ \\ x = -\dfrac{4}{14} \\ \\=> x = -\dfrac{2}{7}$

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$\dfrac{x - 2}{4} + \dfrac{2x + 8}{5} = 5 \\ \\ \\ \dfrac{13x + 22}{20} - 5 = 0 \\ \\ \\ \dfrac{13x - 78}{20} = 0 \\ \\ \\ 13x - 78 = 0 \\ \\ 13x = 78 \\ \\ x = \dfrac{78}{13} \\ \\=> x = 6$

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$d) \\ \\ \dfrac{x + 1}{x - 1} + \dfrac{2x - 5}{x - 3} = 3 \\ \\ \\ \dfrac{3x^2 - 9x + 2}{x^2 - 4x +3} = 3 \\ \\ \\ \dfrac{3x^2 - 9x + 2}{x^2 - 4x +3} - 3 = 0 \\ \\ \\ \dfrac{3x - 7}{(x-1)(x - 3)} = 0 \\ \\ \\ 3x - 7 = 0 \\ \\ 3x = 7 \\ \\=> x = \dfrac{7}{3}$