6.3 ADDING and SUBTRACTING Rational Expressions REVIEW. When you ADD rational numbers (fractions): 1) Write each number with common denominator
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1 6.3 ADDING and SUBTRACTING Rational REVIEW When you ADD rational numbers (fractions): 1) Write each number with common denominator =
2 6.3 ADDING and SUBTRACTING Rational = REVIEW When you ADD rational numbers (fractions): 2) ADD numerators together, COPY the denominators
3 6.3 ADDING and SUBTRACTING Rational = REVIEW When you ADD rational numbers (fractions): 3) SIMPLIFY /CANCEL if possible
4 6.3 ADDING and SUBTRACTING Rational When you SUBTRACT rational numbers (fractions): 1) Write each number with common denominator =
5 6.3 ADDING and SUBTRACTING Rational When you SUBTRACT rational numbers (fractions): 2) SUBTRACT numerators from one another, COPY the denominators =
6 6.3 ADDING and SUBTRACTING Rational When you SUBTRACT rational numbers (fractions): 3) SIMPLIFY /CANCEL if possible =
7 20xy 8x² Equivalent Rational Expression When a rational expression is divided or multiplied by 1 (in a form of monomial or binomial), it does not change the value of the rational expressions = = 20xy 8x² x x x = 20x²y 8x³ = 20xy 8x² 2x : 2x = 10y 4x All of these three expressions are equivalent rational expression
8 6.3 ADDING and SUBTRACTING Rational 1 c² + 5 c² = 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR LOWEST COMMON DENOMINATOR) 4) ADD/SUBTRACT numerators, COPY the denominators 5) SIMPLIFY /CANCEL if possible
9 2a b 6.3 ADDING and SUBTRACTING Rational - a 1 b = 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR LOWEST COMMON DENOMINATOR) 4) ADD/SUBTRACT numerators, COPY the denominators 5) SIMPLIFY /CANCEL if possible
10 6.3 ADDING and SUBTRACTING Rational 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible
11 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible
12 6.3 ADDING and SUBTRACTING Rational 1 c + 5 c² = 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR LOWEST COMMON DENOMINATOR) 4) ADD numerators together, COPY the denominators 5) SIMPLIFY /CANCEL if possible
13 6.3 ADDING and SUBTRACTING Rational The non permissible value is c = 0 1 c + 5 c² = c² + 5c c 3 c 3 = 1) FACTOR if possible 2) NPVs c² + 5c c 3 = c+5 c 2 3) Write each number with COMMON DENOMINATOR (OR LOWEST COMMON DENOMINATOR) 4) ADD numerators together, COPY the denominators 5) SIMPLIFY /CANCEL if possible
14 6.3 ADDING and SUBTRACTING Rational The non permissible value is c = 0 1 c + 5 c² = c c c 2 = 1) FACTOR if possible 2) NPVs c + 5 c 2 3) Write each number with COMMON DENOMINATOR (OR LOWEST COMMON DENOMINATOR) 4) ADD numerators together, COPY the denominators 5) SIMPLIFY /CANCEL if possible
15 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible
16 The non permissible value is x = 0 and y = 0 1 6xy ADDING and SUBTRACTING Rational 2 15x² = 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible ( 1 6xy 15x² 15x² ) ( 2 15x² 6xy 6xy )= 15x² 90x³y - 12xy 15x² 12xy 90x³y = 90x³y = 3x(5x 4y) 90x³y 5x 4y 30x²y =
17 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible
18 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible
19 1) FACTOR if possible 2) NPVs 3) Write each number with COMMON DENOMINATOR (OR COMMON MULTIPLE) 4) SUBTRACT numerators from one another, COPY the denominators 5) SIMPLIFY /CANCEL if possible
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PreCalc 12 Chapter 2 Review Pack v2 Answer Section
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5. In the Cartesian plane, a line runs through the points (5, 6) and (-2, -2). What is the slope of the line?
Slope review Using two points to find the slope In mathematics, the slope of a line is often called m. We can find the slope if we have two points on the line. We'll call the first point and the second