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Math Topics

Elementary Algebra

Rational Expressions

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1
Reducing Rational Expressions to Lowest Terms

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2
Multiplication and Division of Rational Expressions

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3
Addition and Subtraction of Rational Expressions

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4
Complex Fractions

Simplify each term and explain how this sequence is related to the Fibonacci sequence: \(1+\displaystyle\frac{1}{1+1}, 1+\displaystyle\frac{1}{1+\displaystyle\frac{1}{1+1}},1+\displaystyle\frac{1}{1+\displaystyle\frac{1}{1+\displaystyle\frac{1}{1+1}}}, \ldots\)

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5
Equations Involving Rational Expressions

**Mini Lecture**

Solve.

\(\displaystyle\frac{x}{3}+\displaystyle\frac{1}{2}=-\displaystyle\frac{1}{2}\)

\(\displaystyle\frac{1}{y}-\displaystyle\frac{1}{2}=-\displaystyle\frac{1}{4}\)

\(1-\displaystyle\frac{8}{x}=-\displaystyle\frac{15}{x^2}\)

\(\displaystyle\frac{8}{x^2-4}+\displaystyle\frac{3}{x+2}=\displaystyle\frac{1}{x-2}\)

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Proportions

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7
Applications

**Mini Lecture**

One number is three times as large as another. The sum of their reciprocals is \(16/3\). Find the numbers.

One plane can travel \(20\) mph faster than another. One of them goes \(285\) miles in the same time it takes the other to go \(255\) miles. What are their speeds?

An inlet pipe can fill a pool in \(12\) hours, while an outlet pipe can empty it in \(15\)hours. If both pipes are left open, how long will it take to fill the pool?

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8
Variation

**Mini Lecture**

\(y\) varies directly as \(x\). If \(y=39\) when \(x=3\), find \(y\) when \(x\) is \(10\).

\(y\) varies inversely as the square of \(x\). If \(y=4\) when \(x=3\), find \(y\) when \(x\) is \(2\).

The power \(P\) is an electric circuit varies directly with the square of the current \(I\). If \(P=30\) when \(I=2\) find \(P\) when \(I=7\).