Vamos resolver passo a passo

x=(4+23)−1x = \left(4 + \frac{2}{3}\right)^{-1}

x=(4+3

2

​)−1

Primeiro somamos:

4=123⇒123+23=1434 = \frac{12}{3} \Rightarrow \frac{12}{3} + \frac{2}{3} = \frac{14}{3}

4=3

12

​⇒3

12

​+3

2

​=3

14

​

Agora aplicamos o expoente −1-1

−1 (inverso):

x=(143)−1=314x = \left(\frac{14}{3}\right)^{-1} = \frac{3}{14}

x=(3

14

​)−1

=14

3

​

314⋅y=1556\frac{3}{14} \cdot y = \frac{15}{56}

14

3

​⋅y=56

15

​

Agora isolamos yy

y:

y=1556÷314y = \frac{15}{56} \div \frac{3}{14}

y=56

15

​÷14

3

​

Multiplicamos pelo inverso:

y=1556×143y = \frac{15}{56} \times \frac{14}{3}

y=56

15

​×3

14

​

Simplificando:

• 14÷56=1/414 \div 56 = 1/4
• 14÷56=1/4

y=154⋅3=1512y = \frac{15}{4 \cdot 3} = \frac{15}{12}

y=4⋅3

15

​=12

15

​

y=54y = \frac{5}{4}

y=4

5

​

y=54y = \frac{5}{4}

y=4

5

​

✔ Alternativa correta: D