Question

17 – Determine o valor de y para que as Expressões $\begin{gathered} \begin{gathered} \:   \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{ \dfrac{3y}{y \: - \: 4} }\end{array}}}} \end{gathered}  \end{gathered}$ e $\begin{gathered} \begin{gathered} \:   \overline{ \boxed{\boxed{ \begin{array}{r}\mathsf{3 \: + \: \dfrac{2}{y } }\end{array}}}} \end{gathered}  \end{gathered}$ sejam iguais, sabendo que y ≠ 0 e y ≠ 4.​

Answer 1

$\displaystyle \sf \frac{3y}{y-4}=3+\frac{2}{y} \\\\\\ \frac{3y}{y-4}=\frac{3y+2}{y} \\\\\\ 3y\cdot y = (y-4)\cdot (3y+2) \\\\ 3y^2=3y^2+2y-12y-8 \\\\ 3y^2-3y^2-10y- 8 = 0 \\\\ 10 y = -8 \\\\ y = \frac{-8}{10} \\\\\ \huge\boxed{\sf \ y = \frac{-4}{5}\ }\checkmark$

Answer 2

Após resolver os cálculos, concluímos que o valor de "y" para que as expressões sejam iguais é $\sf y=-\dfrac{4}{5}\,\cdot$

Para resolver esse exercício, basta iguala as expressões, veja:

$\sf\boxed{\sf\dfrac{3y}{y-4}}\quad e\quad\boxed{\sf3+\dfrac{2}{y}}~, com~y\neq0;\,y\neq4$

$\mathsf{\dfrac{3y}{y-4}=3+\dfrac{2}{y} }$

$\mathsf{\dfrac{3y}{y-4} -\dfrac{2}{y}=3}$

$\mathsf{\dfrac{3y^2-2(y-4)}{y(y-4)}=3 }$

$\mathsf{ \dfrac{ 3y^2 -2y+8}{y(y-4)}=3}$

$\mathsf{3y^2-2y+8=3y(y-4) }$

$\mathsf{\diagdown\!\!\!\!\!\!3y^2-2y+8=\diagdown\!\!\!\!\!\!3y^2-12y }$

$\mathsf{-2y+8=-12y }$

$\mathsf{ -2y+12y= -8}$

$\mathsf{ 10y= -8}$

$\mathsf{ y=-\dfrac{8}{10}}$

$\boxed{\boxed{\sf y=-\dfrac{4}{5}}}$

Logo, o valor de "y" para que as expressões sejam iguais é $\sf y=-\dfrac{4}{5}\,\cdot$

Aprenda mais em:

https://brainly.com.br/tarefa/32389353