Algebraic Fractions

Undefined/Simplify

100

When is the following fraction Undefined?

                       

3/(x+4)

x=-4

200

^Simplify:

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

2/(x-2)

300

When is the following Undefined?

(x+5)/(x^2-3x-10)

x=5 and x=-2

400

Simplify:

(36-4x^2)/(2x^2-6x)

(-2(3+x))/x

500

Simplify:

(3x^2+3x-18)/(6x^2+24x+18)

 

(x+2)/(2(x+1))

Multiplying/Dividing

100

4/(2x+8)*(6x^2+24x)/(8x^2)

 

(3x)/2

200

(x^2-16)/(9-x)*(x^2+x-90)/(x^2+14x+40)

-(x-4)

300

(10x-30)/(5x+20)-:(x^2-9)/(x^2+7x+12)

2

400

(10x^2-20x)/(40x^3-80x^2)-:(6x+30)/(16x^3+80x^2)

2/3

500

(18-8x^2)/(2x^2+x-3)*(3x^2+9x-12)/(4x^2+10x-24)

-3

 

Add/Subtract

100

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

x+1

200

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

x+3

300

(x+2)/3-(x-5)/6

(x+9)/6

400

(r+6)/5-(r+1)/4

(-r+19)/20

500

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

x/6

Tougher Add/Subtract

100

6/(x-1)-(12)/(x^2-1)

1/(x+1)

200

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

1/(x-1)

300

16/(4x+8)-2/(x+2)

2/(x+2)

400

(x+2)/(x^2+5x)+3/x

(4x+17)/(x(x+5))

500

x/((x+1)(x-3))-2/((x-5)(x+1))

(x-6)/((x-3)(x-5)

Solve

100

3/4+4/x=1/x

x=-4

200

(2x+5)/(x+4)=(x+1)/x

x=2 and x=-2

300

(x-4)/6+(x-2)/10=31/15

x=11

400

16/x=x-6

x=8 and x=-2

500

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

x=1 and x=4