Rational Functions

Simplify Rational Functions and state restrictions

100

(4d^2+8d)/(2d)

2(d+2)

d!=0

200

(6x^3+6x^2)/(2x^3-2x)

(3x)/(x-1);x!=-1,0,1

300

((x+3)(x-3)(x^3+9x))/(x^2+9)

x(x+3)(x-3)

"defined for all real numbers"

400

(x^2+13x+40)/(x^2-2x-35)

(x+8)/(x-7);x!=-5,7

500

(4x^2-12x+9)/(2x^2+15x-27)

(2x-3)/(x+9);x!=-9,3/2

Multiply/Divide Rational Functions (state restrictions for multiplication)

100

(x^2-16)/(x+3)*(x^2-9)/(x-4)

(x+4)(x-3);x!=-3,4

200

(7x^4)/(24y^5)-:(21x)/(12y^4)

(x^3)/(6y)

300

(x^2)/(x+3) *(x^2+4x+3)/((x^2-2x)

(x(x+1)]/(x-2);x!=-3,0,2

400

(2x^2+5x-3)/(x^2-4x)*(2x^3-8x^2)/(x^2+6x+9)

(2x(2x-1))/(x+3);x!=-3,0,4

500

(x^2-81)/(4x^2+27x-7)-:(x^2-5x-36)/(x^2+11x+28)

(x+9)/(4x-1)

Graph Rational Functions

100

Find the VA(s), HA(s), hole(s) and intercepts of the graph: 

f(x)=(x+3)/(x-2)

VA:x=2; HA:y=1; Hole:none

Intercepts: (0,-3/2) (-3,0)

200

Describe the VA(s), HA(s), hole(s) and intercept(s) of the graph:  f(x)=(x+3)/(x^2-9)  

VA:x=3; HA:y=0;

Hole:(-3,-1/6)

Intercepts: (0,-1/3), no x-intercept

300

Describe the VA(s), HA(s), hole(s) and intercept(s) of the graph:

y=(x^2+4x)/(x^2+3x-4)

VA:x=1; HA:y=1;

Hole:(-4, 4/5)

Intercepts: (0,0)

400

Describe the VA(s), HA(s), hole(s) and intercept(s) of the graph:  f(x)=(3x^2-5x-2)/(x^2-3x+2) 

VA:x=1; HA:y=3

Hole: (2,7)

Intercepts: (0,-1), (-1/3,0)

500

Write the equation in standard form (not factored) for the graph that has VA @ x=2, HA @ y=1, Hole @ (-3, 2/5), y-intercept @ (0,-1/2) and x-intercept @ (-1,0)

f(x)=(x^2+4x+3)/(x^2+x-6)

Add/Subtract Rational Functions

100

"State the LCD and then perform the operation" 

(3)/(12y)+(9)/(24)

"LCD"=24y;

(6+9y)/(24y)

200

"State the LCD and then perform the operation" 

1/x+(x-1)/5

"LCD"=5x

(x^2-x+5)/(5x)

300

"State the LCD and then perform the operation" 

(3)/(x+4)-(1)/(x+6)

"LCD"=(x+6)(x+4)

((2x+14))/((x+6)(x+4)

400

"State the LCD and then perform the operation" 

x/(x^2-2x-8)-(4+x-x^2)/(x^2-2x-8)

"LCD"=(x-4)(x+2)

(x-2)/(x-4

500

"State the LCD and then perform the operation" 

(x+1)/(4x^2-9)-(4)/(2x-3)

"LCD"=(2x-3)(2x+3)

(-7x-11)/{(2x-3)(2x+3)

Solve Rational Functions

100

(x+6)/(4x)+(3)/(2x)=(x+4)/(2x)

x=4

200

(1)/(x^2-x)+(1)/(x)=(5)/(x^2-x)

x=5

300

(1)/(x)+(3x+12)/(x^2-5x)=(7x-56)/(x^2-5x)

x=21

400

(x+4)/(4)+(x-1)/(4)=(x+4)/(4x)

x=-2

x=1

500

1/(x-1)=(x)/(x+3)+3/5

x=2

x=-3/2