Search Header Logo
6.4 - Rational Expressions

6.4 - Rational Expressions

Assessment

Presentation

Mathematics

8th - 11th Grade

Medium

CCSS
HSA.APR.D.6

Standards-aligned

Created by

Steve Dull

Used 5+ times

FREE Resource

13 Slides • 2 Questions

1

6.4 - Rational Expressions

Slide image

2

Rational Expression

A quotient of two polynomials

3

Examples

  •  5x\frac{5}{x}  

  •  x24x+2\frac{x^2-4}{x+2}  

  •  x+3x7\frac{x+3}{x-7}  

4

Because rational expressions are ratios of polynomials, you can simplify them the same way you simplify fractions

  •  924=3383=38\frac{9}{24}=\frac{3\cdot3}{8\cdot3}=\frac{3}{8}  

  • Divide out common factors in the numerator and denominator

5

Example 1

  •  x22x3x2+5x+4\frac{x^2-2x-3}{x^2+5x+4}  

  •  (x3)(x+1)(x+1)(x+4)\frac{\left(x-3\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}  

  •  (x3)(x+4)\frac{\left(x-3\right)}{\left(x+4\right)}  

  • STOP!

6

We can't simplify x3x+4\frac{x-3}{x+4}  any further.

  • Specifically, we cannot divide out the x terms.

  • That would be like saying I'm going to simplify  6663\frac{66}{63}  by dividing out the 6s and saying it's equal to  63=2\frac{6}{3}=2  

  • It doesn't work that way

7

One other thing

  • We have to check for values of x that restricted from the domain.

  • In  (x3)(x+1)(x+1)(x+4)\frac{\left(x-3\right)\left(x+1\right)}{\left(x+1\right)\left(x+4\right)}  , the expression is undefined at x=-1 and x=-4 because those values of x make the factors (x+1) and (x+4) equal to 0, making the whole denominator equal to 0. And division by 0 is undefined.

8

You try

9

Multiple Choice

Simplify x2+8x+15x2+x6\frac{x^2+8x+15}{x^2+x-6}  

1

 8x+15x6\frac{8x+15}{x-6}  

2

 x+5x2\frac{x+5}{x-2}  

3

 7x+97x+9  

4

 x+3x2\frac{x+3}{x-2}  

10

We can also multiply and divide rational expressions

11

Slide image

12

You try

13

Multiple Choice

Multiply 10x40x26x+8x+35x+15\frac{10x-40}{x^2-6x+8}\cdot\frac{x+3}{5x+15}  


1

 105\frac{10}{5}  

2

 5x105x-10  

3

 2x2\frac{2}{x-2}  

4

 1x\frac{1}{x}  

14

Slide image

15

We'll get a chance to practice dividing rational expressions in the Math XL set after the break

6.4 - Rational Expressions

Slide image

Show answer

Auto Play

Slide 1 / 15

SLIDE