Divide (using Complex Fractions - ((((5)/(6)x+3)/((1)/(6)-y)))/((3x)/(4y)) Paragraph I U_

Simplify Numerator and Denominator: Step 1: Simplify the numerator and denominator separately. Numerator: (5/6)x + 3 Denominator: (1/6) - yCombine into Single Fraction: Step 2: Combine the numerator and denominator into a single fraction. Numerator: (5/6)x + 3 Denominator: (1/6) - y Fraction: ((5/6)x + 3) / ((1/6) - y)Multiply by Reciprocal: Step 3: Multiply by the reciprocal of the denominator of the main fraction. Reciprocal of ((3x)/(4y)) is ((4y)/(3x)) New Fraction: [((5/6)x + 3) / ((1/6) - y)] * ((4y)/(3x))Simplify Expression: Step 4: Simplify the expression by multiplying the numerators and denominators. Numerator: (5/6)x + 3 Denominator: (1/6) - y Multiply: [(5/6)x + 3] * (4y) / [(1/6) - y] * (3x) = (20yx/18 + 12y/3x) / (3x/18 - 3xy/6) = (20yx + 36y) / (x - 3xy)

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Divide (using Complex Fractions) - $\newline$ $\frac{\left(\frac{5}{6}x+3\right)}{\left(\frac{1}{6}-y\right)}$ / $\frac{3x}{4y}$ $\newline$

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Algebra 1

Multiplication with rational exponents

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Q. Divide (using Complex Fractions) -

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\frac{\left(\frac{5}{6}x+3\right)}{\left(\frac{1}{6}-y\right)}

\frac{3x}{4y}

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Simplify Numerator and Denominator: Step $1$ : Simplify the numerator and denominator separately. $\newline$ Numerator: $(\frac{5}{6})x + 3$ $\newline$ Denominator: $(\frac{1}{6}) - y$
Combine into Single Fraction: Step $2$ : Combine the numerator and denominator into a single fraction. $\newline$ Numerator: $(\frac{5}{6})x + 3$ $\newline$ Denominator: $(\frac{1}{6}) - y$ $\newline$ Fraction: $\frac{(\frac{5}{6})x + 3}{(\frac{1}{6}) - y}$
Multiply by Reciprocal: Step $3$ : Multiply by the reciprocal of the denominator of the main fraction. $\newline$ Reciprocal of $\left(\frac{3x}{4y}\right)$ is $\left(\frac{4y}{3x}\right)$ $\newline$ New Fraction: $\left[\left(\frac{5}{6}x + 3\right) / \left(\frac{1}{6} - y\right)\right] * \left(\frac{4y}{3x}\right)$
Simplify Expression: Step $4$ : Simplify the expression by multiplying the numerators and denominators. $\newline$ Numerator: $(\frac{5}{6})x + 3$ $\newline$ Denominator: $(\frac{1}{6}) - y$ $\newline$ Multiply: $\left[\left(\frac{5}{6}\right)x + 3\right] \times (4y) / \left[\left(\frac{1}{6}\right) - y\right] \times (3x)$ $\newline$ = $\frac{20yx}{18} + \frac{12y}{3x} / \frac{3x}{18} - \frac{3xy}{6}$ $\newline$ = $\frac{20yx + 36y}{x - 3xy}$