Question

determine o valor real de y para que as expressões 3y/y-4 e 3+ 2/y sejam iguais, sabendo que y = 0 e y = 4​

Answer 1

Resposta:

y = -4/5

Explicação passo-a-passo:

$\frac{3y}{y-4} = 3+ \frac{2}{y} \\\\\frac{3y}{y-4} = \frac{3y + 2}{y} \\\\3y^2 = (3y +2)(y-4)\\\\3y^2 = 3y^2 - 12y + 2y - 8\\\\3y^2 = 3y^2 -10y - 8\\\\10y = -8\\\\y = -8/10\\\\y = -4/5$

Verificando

$\frac{3 (-4/5)}{(-4/5) - 4} = 3 + \frac{2}{(-4/5)} \\\\\frac{-12/5}{-24/5} = 3 - \frac{10}{4} \\\\\frac{12}{24} =\frac{12-10}{4}\\\\\frac{1}{2} = \frac{1}{2}$

Answer 2

Resposta:

- 4/5

Explicação passo a passo:

3y/( y-4) = 3/1 + 2/y

3y/y(y-4) = 3y (y-4) +2 ( y-4) / y(y-4)

3y^2 = 3y^2 - 12y + 12y - 8

3y^2 - 3y^2 - 12y + 2 y = - 8

10y = -8

y= -8/10 (:2)

y= -4/5

MMC

(y-4)  y(y- 4 )

y