chapter 11 rational expressions and equations by: nick fanning and rhyan gelinas
TRANSCRIPT
Chapter 11Rational Expressions and
Equations
By: Nick Fanning and Rhyan Gelinas
11.1 Proportions
• Reciprocal Property of Proportionsa/b = c/d then b/a = d/c
• Cross Product Propertya/b = c/d then ad = bc
11.1 Proportions
• Ex 1) 2/3 = 4/6 then
3/2 = 6/4• Ex 2)
2/3 = 4/6 then
2*6 = 3*4
11.2 Direct and Inverse Variation
• Direct Variation– The variables x and y vary directly if and only if for a
constant k – y/x = k or y =kx where k ≠ 0
Ex) Find an equation that relations x and y such that x and y vary directly and y = 4 and x = 2
Step 1: Write direct variation model
y/x = kStep 2: Substitute
4/2 = KStep 3: Solve
k = 2
11.2 Direct and Inverse Variation
• Inverse Variation– The variable x and y vary inversely if for a constant k– xy = k or y = k/x where k ≠ 0
Ex) Find an equation that relations x and y such that x and y vary inversly and y = 4 and x = 2
Step 1: Write inverse variation model xy = k
Step 2: Substitute4 * 2 = K
Step 3: Solvek = 8
11.3 Simplifying Rational Expressions
• Rational Number = number that can be written as the quotient of 2 integers
• Rational Expression = a number whose number and denominator are a nonzero polynomial
11.3 Simplifying Rational Expressions
• Simplifying Rational Expressions ac/ bc = a * c / b * c = a/b
Ex) Simplify 14x/7
Step 1: Write equation
14x/7
Step 2: Rationalize
2 * 7 * x / 7
Step 3: Simplify
2x
11.4 Multiplying and Dividing Rational Expressions
• Multiplicationa/b * c/d = ac/bd
Ex) Multiply 4x/2 * 2x/4
Step 1: Write equation
4x/2 * 2x/4
Step 2: Multiply
8x/8
Step 3: Simplify
x
11.4 Multiplying and Dividing Rational Expressions
• Divisiona/b ÷ c/d = a/b * d/c
Ex) Divide 4x/2 ÷ 2x/4
Step 1: Write equation
4x/2 ÷ 2x/4
Step 2: Multiply
4x/2 * 4/2x = 16x/ 4x
Step 3: Simplify
4
11.5 Adding and Subtracting with Like Denominators
• Additiona/c + b/c = (a+b) /c
Ex) Add 5/2x + x-5/2x
Step 1: Write equation
5/2x + x-5/2x
Step 2: Add
x/2x
Step 3: Simplify
1/2
11.5 Adding and Subtracting with Like Denominators
• Subtractiona/c – b/c = (a-b) /c
Ex) Subtract 5/2x + x/2xStep 1: Write equation
5/2x - x/2x Step 2: Subtract
5-x/2xStep 3: Simplify
(5-x)/2x
11.6 Adding and Subtracting unlike Denominators
• LCD = Least Common Denominator– Use to add and subtract unlike denominators
Ex) Find the LCD of 1/12x and (2+x)/40xStep 1: Factor
12x = 2^2 * 3 * x40x^4 = 2^3 * 5 * x^4
Step 2: Find the highest power of each factor
2^3, 3, 5, x^4Step 3: Multiply
2^3 *3 *5 *x^4 = 120x^4
11.7 Rational Equations
• Rational Equation = equation that contains rational expressions
Ex) Solve 5/(y+2) = y/3Step 1: Write
5/(y+2) = y/3Step 2: Cross Multiply
5(3) = y(y+2)Step 3: Simplify
y^2 + 2y = 15Step 4: Write
y^2 +2y -15 = 0Step 5: Factor
(y+5)(y-3) = 0Answer = y = -5, 3
Links
• Ration Practice– http://www.regentsprep.org/Regents/Math/rati
o/PracRatio.htm• Direct and Inverse Variation
– http://www.mathsteacher.com.au/year10/ch17_variation/05_directvariation/25direct.htm
• Fraction Practice– http://www.aaamath.com/fra.html