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= 6x2 – 5x – 21 = x2 – 121 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2)Find the product. (2x + 3)(3x – 7) (x – 11)(x + 11) = 6x2 – 5x – 21 = x2 – 121 Factor. 3. 10x + 25 4. 28x2 + 35x 5. x3 + 2x2 + 4x + 8 = 5(2x + 5) = 7x(4x + 5) = (x2 + 4) (x + 2) x2 + 11x + 30 7. x2 – 4x – 32 = (x + 6) (x + 5) = (x + 4) (x – 8)
More warm-up Solve the following equation (USE Factoring)
More Warm-up Simplify the fraction Standard: MM1A3e
Simplifying rational expressionsA fraction whose numerator and denominator are nonzero polynomials Standard: MM1A3e
Simplest Form When a rational expression’s numerator and denominator have no factors in common (other than 1). Process: Factor, then cancel. Standard: MM1A3e
1. Simplify a Rational ExpressionReduce the numbers and subtract the exponents. Where the larger one is, is where the leftovers go. Standard: MM1A3e
2. Simplify a Rational ExpressionFactor the top Cross out the common factor x. Standard: MM1A3e
3. Simplify a Rational ExpressionFactor the bottom Cross out the common factor x. Standard: MM1A3e
4. Simplify a Rational ExpressionFactor the top Cross out the common factors of 5 and x. Standard: MM1A3e
5. Simplify a Rational ExpressionFactor the top and bottom Cross out the common factor (x + 4) Standard: MM1A3e
Recognize Opposite FactorsWhen you have opposite factors, you will have to factor out a negative so that you can cancel. Standard: MM1A3e
6. Opposite Factors Factor the bottom(1 – x) on the top and (x – 1) on the bottom are opposites. Factor out a negative so they will cancel. Standard: MM1A3e
Practice #7 Standard: MM1A3e
Practice #8 Standard: MM1A3e
Practice #9 Standard: MM1A3e
Practice #10 Standard: MM1A3e
Practice #11 Standard: MM1A3e
Practice #12 Standard: MM1A3e
Notes Over 9.4 Simplifying a Rational Expression Simplify the expression if possible. Rational Expression A fraction whose numerator and denominator are.
Algebra 11-3 and Simplifying Rational Expressions A rational expression is an algebraic fraction whose numerator and denominator are polynomials.
Simplify Rational Expressions
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12-6 Rational Expressions with Like Denominators Objective: Students will be able to add and subtract rational expressions with like denominators.
Use definition of zero and negative exponents EXAMPLE 1 a. 3 – 2 Definition of negative exponents 1 9 = Evaluate exponent. b. (–7) 0 Definition of zero.
6.2A- Operations for Fractions Adding & Subtracting – Create a COMMON DENOMINATOR – ADD or SUBTRACT 2 TOPS (Numerators) – KEEP the common denominator (bottom)
9.1 Simplifying Rational Expressions Objectives 1. simplify rational expressions. 2. simplify complex fractions.
Reducing Fractions. Factor A number that is multiplied by another number to find a product. Factors of 24 are (1,2, 3, 4, 6, 8, 12, 24).
RATIONAL EXPRESSIONS. Definition of a Rational Expression A rational number is defined as the ratio of two integers, where q ≠ 0 Examples of rational.
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Add & Subtract Rationals – Common Denominator To add or subtract rational expressions with common denominators: 1) Add or subtract the numerators 2) Write.
Fractional Expressions Section 1.4. Objectives Simplify fractional expressions. Multiply and divide fractional expressions. Add and subtract fractional.
Multiplying, Dividing, Adding, Subtracting Rational Expressions
9.1 Multiplying and Dividing Rational Expressions ©2001 by R. Villar All Rights Reserved.
Finding a Common Denominator
Do Now: Solve for x in the following equation: Hint: and.
Section 6.3 Adding & Subtracting Rational Expressions Adding & Subtracting RE’s with Same Denominator Finding the LCD of 2 or more Polynomial Denominators.
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Multiplying & Dividing Rational Expressions. Simplified form of a rational expression - Means the numerator and denominator have NO common factors. To.
Warm-Up x 3x +12 2x – (4 – 5x) = 3(x + 4) 2x – 4 + 5x = 3x + 12
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