Rational Functions

Simplify Rational Functions

100

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

^d/₂ +4

200

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

(3x)/(x-1

300

(x^2+9x+18)/(x+6)

x+3

400

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

(x+8)/(x-7)

500

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

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

Multiply/Divide Rational Functions

100

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

(x{x+1}]/(x-2)

200

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

(x^3)/(6y)

300

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

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

400

(30x^2-60x^2)/(3x)-:(2x^3-16x^2+24x)

(5)/(x-6)

500

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

(2x{2x-1})/(x+3)

Extraneous solutions

100

(1)/(2x-3) = (3)/(x+11)

no

200

is the following an extraneous solution

    

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

no

300

extraneous solution?

(x)/(2x-3)=(3x)/(x+11)

Hole= x=-4

400

extraneous solution

(x-1)/(2x-3)=(3x+2)/(x+11)

 

yes

500

extraneous?

(2x+6)/8x=(2x+12)/12x

 

yes

Add/Subtract Rational Equations

100

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

15/24

200

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

{(x-3)(x+2)}/(x(x+6)

300

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

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

400

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

(2{x+7})/({(x+6)(x+4)}

500

1/x+(x-1)/5

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

Solve Rational Equations

100

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

x=4

200

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

x=-2

x=1

300

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

x=21

400

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

x=5

500

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

x=-1