1. Simplify the expression: 𝑥 2 −9 3 3−𝑥 8
Problem of the Day

2. Simplify each expression
Problem of the Day

3. Section 8-2 Adding and Subtracting Rational Expressions

4. Then Now Objectives You added and subtracted polynomial expressions.
Determine the LCM of polynomials.
Add and subtract rational expressions.

5. Common Core State Standards
Content Standards
A.APR.7 – Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.
Mathematical Practices
3) Construct viable arguments and critique the reasoning of others.
Common Core State Standards

6. Add and Subtract Fractions (without a calculator)!
− 1 4 Just as with rational numbers in fractional form, to add or subtract two rational expressions that have unlike denominators, you must first find the least common denominator.
Add and Subtract Fractions (without a calculator)!

7. Example 1 (LCM of Monomials)
Find the LCM of each set of monomials. 12𝑎 2 and 15𝑎 16 𝑐 5 and 24 𝑐 3
Example 1 (LCM of Monomials)

8. Add and Subtract Rational Expressions
To add or subtract rational expressions, find the least common denominator (LCD). Rewrite each expression with the LCD. Then add or subtract.
Add and Subtract Rational Expressions

9. Example 2 (Monomial Denominators)
Simplify: 4 5𝑎 3 + 𝑎+9 10𝑎
Example 2 (Monomial Denominators)

10. Example 2 (Monomial Denominators)
Simplify: 7 12𝑏 2 − 𝑏+3 8𝑏
Example 2 (Monomial Denominators)

11. Example 2 (Monomial Denominators)
Simplify: 5𝑐 2 6𝑐 − 𝑐−8 14 𝑐 2
Example 2 (Monomial Denominators)

12. Example 1 (LCM of Polynomials)
Find the LCM of each set of polynomials. 𝑥 2 −16 and 𝑥+4 2𝑥−12 and 𝑥 2 −4𝑥−12
Example 1 (LCM of Polynomials)

13. Example 3 (Polynomial Denominators)
Simplify:
Example 3 (Polynomial Denominators)

14. Example 3 (Polynomial Denominators)
Simplify:
Example 3 (Polynomial Denominators)

15. Example 3 (Polynomial Denominators)
Simplify:
Example 3 (Polynomial Denominators)

16. Example 3 (Application Problems)
ELECTRIC POTENTIAL The electrical potential function between two electrons is given by a formula that has the form 1 𝑟 − 𝑟 . Simplify this expression.
Example 3 (Application Problems)

17. Example 3 (Application Problems)
GEOMETRY Find the perimeter of the rectangle.
Example 3 (Application Problems)

18. Example 3 (Application Problems)
OIL PRODUCTION Managers of an oil company have estimated that oil will be pumped from a certain well at a rate based on the function 𝑅 𝑥 = 20 𝑥 + 200𝑥 3𝑥 , where R(x) is the rate of production in thousands of barrels per year x years after pumping begins.
Simplify R(x).
CHALLENGE: At what rate will oil be pumping from the well in 50 years?
Example 3 (Application Problems)

19. Section 8-2 Worksheet
Homework