Question

If ( 1 /2 ) −4 x x/y = ( −3/ 2 ) −2 ÷ ( 2/ 5 ) −2 then find ( x/y ) −2​

Answer 1

★ Solution :-

First, we should find the value of the fraction x/y.

$\sf \leadsto \dfrac{1}{2} - 4 \times \dfrac{x}{y} = \dfrac{-3}{2} - 2 \div \dfrac{2}{5} - 2$

$\sf \leadsto \dfrac{1 - 8}{2} \times \dfrac{x}{y} = \dfrac{-3}{2} - 2 \times \dfrac{5}{2} - 2$

$\sf \leadsto \dfrac{-7}{2} \times \dfrac{x}{y} = \dfrac{-3}{2} - 5 - 2$

$\sf \leadsto \dfrac{-7}{2} \times \dfrac{x}{y} = \dfrac{-3 - 10 - 4}{2}$

$\sf \leadsto \dfrac{-7}{2} \times \dfrac{x}{y} = \dfrac{-17}{2}$

$\sf \leadsto \dfrac{x}{y} = \dfrac{-17}{2} \div \dfrac{-7}{2}$

$\sf \leadsto \dfrac{x}{y} = \dfrac{-17}{2} \times \dfrac{2}{-7}$

$\sf \leadsto \dfrac{x}{y} = \dfrac{17}{7}$

Now, we can find the value of $\sf \dfrac{x}{y} - 2$

$\sf \leadsto \dfrac{x}{y} - 2$

$\sf \leadsto \dfrac{17}{7} - 2$

$\sf \leadsto \dfrac{17 - 14}{7}$

$\sf \leadsto \dfrac{3}{7}$

Therefore, the answer is $\sf \dfrac{3}{7}$.