Option b: [tex]\frac{2(y-2 x)}{3 y-5 x}[/tex] is the expression which is equivalent to [tex]\frac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{y}+\frac{3}{x}}[/tex]
Explanation:
The expression is [tex]\frac{\frac{2}{x}-\frac{4}{y}}{-\frac{5}{y}+\frac{3}{x}}[/tex]
To solve the expression, let us take LCM in both numerator and denominator.
Thus, we have,
[tex]\frac{\left(\frac{2 y-4 x}{x y}\right)}{\left(\frac{3 y-5 x}{x y}\right)}[/tex]
Dividing both fractions, we have,
[tex]\frac{2y-4x}{ 3y-5x}[/tex]
From numerator, let us take the common term 2 out,
[tex]\frac{2(y-2 x)}{3 y-5 x}[/tex]
Thus, the expression equivalent to [tex]\frac{\frac{2}{x}-\frac{4}{y}}{\frac{-5}{y}+\frac{3}{x}}[/tex] is [tex]\frac{2(y-2 x)}{3 y-5 x}[/tex]
Hence, Option b is the correct answer.
