The equivalent expression of the complex fraction is [tex]\boxed{\frac{{2y - 4x}}{{ - 5x + 3y}}}.[/tex]
Further explanation:
Given:
The expression is [tex]\dfrac{{\dfrac{2}{x} - \dfrac{4}{y}}}{{ - \dfrac{5}{y} + \dfrac{3}{x}}}.[/tex]
Explanation:
The given expression is [tex]\dfrac{{\dfrac{2}{x} - \dfrac{4}{y}}}{{ - \dfrac{5}{y} + \dfrac{3}{x}}}.[/tex]
Consider the numerator [tex]\dfrac{2}{x} - \dfrac{4}{y}[/tex] of the fraction as A.
Consider the denominator [tex]\dfrac{3}{x} - \dfrac{5}{y}[/tex] of the fraction as B.
Solve the numerator of the fraction,
[tex]\begin{aligned}A&= \frac{2}{x}- \frac{4}{y}\\&= \frac{{2y - 4x}}{{xy}}\\\end{aligned}[/tex]
Solve the denominator of the complex fraction,
[tex]\begin{aligned}B&= - \frac{5}{y} + \frac{3}{x}\\&= \frac{{ - 5x + 3y}}{{xy}}\\\end{aligned}[/tex]
Divide the numerator and the denominator of the fraction to obtain the equivalent expression.
[tex]\begin{aligned}{\text{Fraction}}=\dfrac{{\dfrac{{2y - 4x}}{{xy}}}}{{\dfrac{{ - 5x + 3y}}{{xy}}}}\\= \dfrac{{2y - 4x}}{{3y - 5x}}\\\end{aligned}[/tex]
The equivalent expression of the complex fraction is [tex]\boxed{\dfrac{{2y - 4x}}{{ - 5x + 3y}}}.[/tex]
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Fractions
Keywords: fraction, simplify, expression, equivalent, complex fraction, [tex](2/x)-(4/y)/(-5/y)+(3/x)[/tex], add, subtraction, denominators, numerators.
