# Simplify -\frac{2}{x}+\frac{\frac{5}{y}}{\frac{3}{y}}-\frac{2}{x}

Simplify $-\frac{2}{x}+\frac{\frac{5}{y}}{\frac{3}{y}}-\frac{2}{x}$
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psor32
$-\frac{2}{x}+\frac{\frac{5}{y}}{\frac{3}{y}}-\frac{2}{x}$
Multiply the numerator and denominator of the middle fraction by y
$=-\frac{2}{x}+\frac{5}{3}-\frac{2}{x}$
Move the negative signs
$=\frac{-2}{x}+\frac{5}{3}+\frac{-2}{x}$
Add the numerators of a fraction with the same denominator
$=\frac{-2-2}{x}+\frac{5}{3}$
Simplify the numerator
$=\frac{-4}{x}+\frac{5}{3}$
$=-\frac{4}{x}+\frac{5}{3}$
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Terry Ray
$-\frac{2}{x}+\frac{\frac{5}{y}}{\frac{3}{y}}-\frac{2}{x}$
$=-\frac{2}{x}+\frac{5}{3}-\frac{2}{x}$
$=\frac{-2}{x}+\frac{5}{3}+\frac{-2}{x}$
$=\frac{-2-2}{x}+\frac{5}{3}$
$=\frac{-4}{x}+\frac{5}{3}$
$=\frac{-12+5x}{3x}$