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Chapter 6: Rational Expressions and Equations
Transcript of Chapter 6: Rational Expressions and Equations
Given a graph or picture, state what type of system it is.
Determine whether a point is a solution to a system.
Determine whether a test point makes an inequality true.
Formula for motion problems. To simplify fractions we cancel common factors: To simplify a rational expression like: We do the same thing, cancel common factors: Rules for multiplying and dividing rational expressions are also the same as multiplying and dividing fractions. We always factor and simplify BEFORE multiplying or dividing, not after. Good news! We don’t actually have to do that! Why? Because… The domain of a rational function excludes any values of the variable that make the denominator zero. To add or subtract fractions we need a common denominator. First we need to find the LCD: Now we can add the fractions: We also need a common denominator to add or subtract rational expressions. A COMPLEX RATIONAL EXPRESSION is a big fraction that has at least one term in the numerator and/or denominator that is itself a rational expression. Compare the methods. To solve a rational equation we will start by clearing all the denominators. Since x = 2 does not make any denaomtiantor zero, we can keep this solution. But maybe we made a mistake, so let’s check: Applications: Formulas & Advanced Ratio Exercises If it takes you three hours to complete your homework, assuming you work at a steady rate, how much of your homework assignment can you complete in one hour? 1/3 of the assignment In general if it takes t hours to complete a task how much of the task can be completed in one hour? 1/t Setting up tables helped us solve mixture and motion problems in earlier chapters. Tables can be helpful in solving rate of work problems as well. If Robert can paint the kitchen in 3 hours and Susan can point the kitchen in 2 hours, how long will it take Robert and Susan to point the kitchen if they work together? If we were to have a quiz at the beigning of a chatper 6 lecture day, what kinds of things might be on it?
Using factoring to simiplify a rational expression.
Finding the domain of a rational expression.
Finding the LCD of two or more rational expressions.