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Simplifying rational expressions and restrictions
- Intro Lesson5:58
- Lesson: 1a1:03
- Lesson: 1b3:52
- Lesson: 1c3:55
- Lesson: 2a4:18
- Lesson: 2b6:40
- Lesson: 3a3:09
- Lesson: 3b3:20
- Lesson: 3c4:29
- Lesson: 4a3:07
- Lesson: 4b2:55
- Lesson: 4c1:59
- Lesson: 5a1:03
- Lesson: 5b2:58
Simplifying rational expressions and restrictions
A rational expression is a fraction that its numerator and/or denominator are polynomials. In this lesson, we will first learn how to find the non-permissible values of the variable in a rational expression. Then, we will how to simplify rational expressions.
Basic Concepts: Common factors of polynomials, Factoring polynomials: ax2+bx+c, Factoring perfect square trinomials: (a+b)2=a2+2ab+b2 or (a−b)2=a2−2ab+b2, Find the difference of squares: (a−b)(a+b)=(a2−b2), Solving polynomial equations
Related Concepts: What is a rational function?, Point of discontinuity, Vertical asymptote, Horizontal asymptote, Solving rational equations
Lessons
⋅ multiplication rule: xa⋅xb=xa+b
⋅ division rule: xbxa=xa−b
⋅ division rule: xbxa=xa−b
- IntroductionWhy is it important to determine the non-permissible values prior to simplifying a rational expression?
- 1.For each rational expression:
i) determine the non-permissible values of the variable, then
ii) simplify the rational expressiona)4x6x3b)x2−8x+155−xc)x2−25x2+13x+40 - 2.For each rational expression:
i) determine the non-permissible values of the variable, then
ii) simplify the rational expressiona)3t2+4t9t3−16tb)x4−10x2+9x2+2x−3 - 3.For each rational expression:
i) determine the non-permissible values of the variable, then
ii) simplify the rational expressiona)3−xx−3b)30−15y5y3−10y2c)6x2−7x−31−9x2 - 4.The area of a rectangular window can be expressed as 4x2+13x+3, while its length can be expressed as 4x+1.a)Find the width of the window.b)If the perimeter of the window is 68 m, what is the value of x?c)If a cleaning company charges $3/m2 for cleaning the window, how much does it cost to clean the window?
- 5.For each rational expression:
i) determine the non-permissible values for y in terms of x , then
ii) simplify, where possible.a)2x−y2x+yb)x2−9y2x−3y
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11.
Operations with Algebraic Fractions
11.1
Simplifying algebraic fractions and restrictions
11.2
Adding and subtracting algebraic fractions
11.3
Multiplying algebraic fractions
11.4
Dividing algebraic fractions
11.5
Solving algebraic fraction equations
11.6
Applications of algebraic fraction equations
11.7
Simplifying complex fractions
11.8
Partial fraction decomposition