Question

Which expression is equivalent to the following complex fraction? (2/x)-(4/y)/(-5/y)+(3/x)

Answer 1

See answer attached.

Answer 2

The equivalent expression of the complex fraction is $\boxed{\frac{{2y - 4x}}{{ - 5x + 3y}}}.$

Further explanation:

Given:

The expression is $\dfrac{{\dfrac{2}{x} - \dfrac{4}{y}}}{{ - \dfrac{5}{y} + \dfrac{3}{x}}}.$

Explanation:

The given expression is $\dfrac{{\dfrac{2}{x} - \dfrac{4}{y}}}{{ - \dfrac{5}{y} + \dfrac{3}{x}}}.$

Consider the numerator $\dfrac{2}{x} - \dfrac{4}{y}$ of the fraction as A.

Consider the denominator $\dfrac{3}{x} - \dfrac{5}{y}$ of the fraction as B.

Solve the numerator of the fraction,

$\begin{aligned}A&= \frac{2}{x}- \frac{4}{y}\\&= \frac{{2y - 4x}}{{xy}}\\\end{aligned}$

Solve the denominator of the complex fraction,

$\begin{aligned}B&= - \frac{5}{y} + \frac{3}{x}\\&= \frac{{ - 5x + 3y}}{{xy}}\\\end{aligned}$

Divide the numerator and the denominator of the fraction to obtain the equivalent expression.

$\begin{aligned}{\text{Fraction}}=\dfrac{{\dfrac{{2y - 4x}}{{xy}}}}{{\dfrac{{ - 5x + 3y}}{{xy}}}}\\= \dfrac{{2y - 4x}}{{3y - 5x}}\\\end{aligned}$

The equivalent expression of the complex fraction is $\boxed{\dfrac{{2y - 4x}}{{ - 5x + 3y}}}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Fractions

Keywords: fraction, simplify, expression, equivalent, complex fraction, $(2/x)-(4/y)/(-5/y)+(3/x)$, add, subtraction, denominators, numerators.