MATH-UA 120 Lecture Notes - Lecture 12: Completing The Square, Nth Root, Rational Function
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Domain: all possible x values of an equation. To find the domain, find all solutions of denominator by setting it equal to zero. **the domain is all real numbers except the solutions. To find the zeros, find the solutions of the numerator by setting it equal to zero. ***anything that is not part of your domain should not be in your zeros*** To divide rational expressions, multiply first expression by reciprocal of second. Lcd is the smallest denominator that each denominator divides evenly into. To solve, multiply entire fraction by lcd and simplify. Method 1: simplify numerator and denominator separately and simplify results. Method 2: multiply all fractions by the lcd of all the fractions in the problem, then simplify. Method 1: simplify each side separately, cross multiply, and solve. **reject solutions that make the original equation 0** Method 2: multiply whole equation by lcd, and solve. Three ways to express relations: graph, table, mapping diagram.
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