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- Rational Expressions

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Get Started Now- 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

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: $ax^2 + bx + c$, Factoring perfect square trinomials: $(a + b)^2 = a^2 + 2ab + b^2$ or $(a - b)^2 = a^2 - 2ab + b^2$, Find the difference of squares: $(a - b)(a + b) = (a^2 - b^2)$, Solving polynomial equations

Related Concepts: What is a rational function?, Point of discontinuity, Vertical asymptote, Horizontal asymptote, Solving rational equations

$\cdot$ multiplication rule: $x^a \cdot x^b=x^{a+b}$

$\cdot$ division rule: $\frac{x^a}{x^b}=x^{a-b}$

$\cdot$ division rule: $\frac{x^a}{x^b}=x^{a-b}$

- 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)$\frac{{6{x^3}}}{{4x}}$b)$\frac{{5 - {x}}}{{{x^2} - 8x + 15}}$c)$\frac{{{x^2} + 13x + 40}}{{{x^2} - 25}}$ - 2.For each rational expression:

i) determine the non-permissible values of the variable, then

ii) simplify the rational expressiona)$\frac{{9{t^3} - 16t}}{{3{t^2} + 4t}}$b)$\frac{{{x^2} + 2x - 3}}{{{x^4} - 10{x^2} + 9}}$ - 3.For each rational expression:

i) determine the non-permissible values of the variable, then

ii) simplify the rational expressiona)$\frac{{x - 3}}{{3 - x}}$b)$\frac{{5{y^3} - 10{y^2}}}{{30 - 15y}}$c)$\frac{{1 - 9{x^2}}}{{6{x^2} - 7x - 3}}$ - 4.The area of a rectangular window can be expressed as $4{x^2} + 13x + 3$, 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 $3/$m^2$ 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)$\frac{{2x + y}}{{2x - y}}$b)$\frac{{x - 3y}}{{{x^2} - 9{y^2}}}$

16.

Rational Expressions

16.1

Simplifying rational expressions and restrictions

16.2

Adding and subtracting rational expressions

16.3

Multiplying rational expressions

16.4

Dividing rational expressions

16.5

Solving rational equations

16.6

Applications of rational equations

16.7

Simplifying complex fractions

16.8

Partial fraction decomposition

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