Pg. 244 Homework

• Pg. 245 #35 – 43 all **Test Friday**Pg. 244 #20 - 26 even, 10, 12

• #2 #4• #6 #8• #10 x = 5 #12 (-∞, -6]U(-5, ∞)• #14 (-4, 1) #16 (-∞, -2)U(1, 2)• #18 [-0.56, 2)U(2, 3.56]

3 2x 13 105

16x

6 2 31

4x

2

2x

4.3 Equations and Inequalities with Rational Functions

Solve:

2

3 2 3 2

A B

x x x x

3 2

1 4 1 4

x A B

x x x x

4.3 Equations and Inequalities with Rational Functions

Steps to solvingRational Equations

• Find a common denominator on each side of the equal sign, if needed.

• Simplify the numerator(s).• Multiply up the denominator(s).• Combine like terms and set the

equation equal to zero.• Solve for x.• Check for the validity of your

answers in the original equation.

Steps to solvingRational Inequalities• Find a common denominator on

each side of the inequality, if needed.

• Simplify the numerator(s).• Subtract over any constants so

the inequality is set to zero.• Find a common denominator.• Simplify the numerator.• Factor the numerator and

denominator.• Create a sign pattern for the

factors to find your answer.

4.3 Equations and Inequalities with Rational Functions

Word Problem!! • Josh rode his bike 17 miles

from his home to Columbus, Ohio, and then completed a 53 mile car trip from Columbus to Mansfield, Ohio. Assume the average rate of the car was 43 mph faster than the average rate of the bike.

– Find an algebraic representation for the total time T required to complete the 70 mile trip as a function of the average rate x of the bike.

– Find a complete graph, including any zeros and asymptotes.

– What values of x make sense for this problem situation?

– If the total trip was one hour and forty minutes, what was the bike’s rate?

4.3 Equations and Inequalities with Rational Functions

Word Problem!! • A cylindrical soda-pop can

of radius r and height h is to hold exactly 355 ml of liquid when completely full. A manufacturer wishes to find the dimensions of the can with the minimum surface area.

– Find an algebraic representation for the surface area S as a function of r.

– What are the restrictions on r for this problem situation?

– Find a complete graph of this problem situation.

– What value of r and h will yield a minimal surface area?