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Rational Expressions and Equations - Coggle Diagram
Rational Expressions and Equations
Definitions
Rational Expression: An algebraic fraction with a numerator and denominator that are polynomials i.e. x^2-4 or 1/x
Rational Equation: an equation containing at least one rational expression i.e. x=(x-3)/(x+1)
Non-Permissible Values: any value for a variable that makes an expression undefined. A value that results in a denominator of zero.
6.1 Non-Permissible Values
Determine what makes the denominator zero
Equivalent Rational Expressions: You can multiply a rational expression by 1 (or say s/s) and the result is equivalent.
Simplifying Rational Expressions: You can simplify rational expressions by dividing both the numerator and the denominator by common factors i.e. AB/AC - B/C
6.2 Multiplying and Dividing Rational Expressions
Multiply: Factor, Reduce then Multiply
Divide: Factor, Find non-permissible values, Multiply by the reciprocal of the divisor, Reduce, Multiply
6.3 Adding and Subtracting Rational Expressions
Denominators are Common: Add and subtract the numerators
Denominators are not the same: Write each expression as an equivalent expression with a common denominator then add and subtract as normal.
LCD: it is easiest to convert to the Lowest Common Denominator
Solving Rational Equations
To Solve Rational Equations: Multiply both sides by a LCD to eliminate the denominator
Rate Problem: Use a table to organize your given data.
Cost Problem: Use a table for data and make equivalent expressions out of the costs
Check for: non-permissible values, extraneous roots and realistic solutions.