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

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Multiplication with rational exponents

Full solution

Q. Divide (using Complex Fractions -

\newline

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

/

\frac{3x}{4y}

\newline

Paragraph

\newline

I

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U_

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: $\left[\left(\frac{5}{6}\right)x + 3\right] \times (4y) / \left[\left(\frac{1}{6}\right) - y\right] \times (3x)$ $\newline$ = $\frac{20yx}{18} + \frac{12y}{3x} / \frac{3x}{18} - \frac{3xy}{6}$ $\newline$ = $\frac{20yx + 36y}{x - 3xy}$

More problems from Multiplication with rational exponents

Question

h(x)=\log _{2}(x)

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Can we use the mean value theorem to say the equation

h^{\prime}(x)=1

has a solution where

1<x<2

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1

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(A) No, since the function is not differentiable on that interval.

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(B) No, since the average rate of change of

h

over the interval

1 \leq x \leq 2

1

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(C) Yes, both conditions for using the mean value theorem have been met.

Posted 3 months ago

Question

What is the sign of

39 \frac{11}{13}+\left(-41 \frac{1}{13}\right) \text { ? }

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-1042+1042 ?

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-18 \frac{9}{17}+\left(-18 \frac{9}{17}\right)

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

\frac{23}{45}+\left(-\frac{23}{45}\right) ?

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

45+(-38)

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-49.8+61.2

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

-1.69+(-1.69) ?

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

What is the sign of

37+(-37)

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1

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(C) Neither positive nor negative-the sum is zero.

Posted 3 months ago

Question

\begin{array}{l} g(x)=\sqrt{2 x-9} \\ g^{\prime}(x)=? \end{array}

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1

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\frac{\sqrt{2 x-9}}{2}

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\frac{1}{\sqrt{2 x-9}}

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\frac{1}{2 \sqrt{2 x-9}}

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\frac{1}{\sqrt{x}}

Posted 3 months ago