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Math Topics
Elementary Algebra
Rational Expressions
1
Reducing Rational Expressions to Lowest Terms
In the introduction to this chapter, we saw that the average cost per check of writing \(x\) checks in one month is given by the rational expression \[A=\dfrac{2.00+0.15x}{x}\] Find the average cost per check if \(8\) checks are written in a month.
2
Multiplication and Division of Rational Expressions
3
Addition and Subtraction of Rational Expressions
4
Complex Fractions
Simplify each term and explain how this sequence is related to the Fibonacci sequence: \(1+\displaystyle\frac{1}{1+1}, 1+\displaystyle\frac{1}{1+\displaystyle\frac{1}{1+1}},1+\displaystyle\frac{1}{1+\displaystyle\frac{1}{1+\displaystyle\frac{1}{1+1}}}, \ldots\)
5
Equations Involving Rational Expressions
Mini Lecture
Solve.
\(\displaystyle\frac{x}{3}+\displaystyle\frac{1}{2}=-\displaystyle\frac{1}{2}\)
\(\displaystyle\frac{1}{y}-\displaystyle\frac{1}{2}=-\displaystyle\frac{1}{4}\)
\(1-\displaystyle\frac{8}{x}=-\displaystyle\frac{15}{x^2}\)
\(\displaystyle\frac{8}{x^2-4}+\displaystyle\frac{3}{x+2}=\displaystyle\frac{1}{x-2}\)
6
Proportions
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?
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 \(I=7\).