Rational Functions

Simplifying...

100

(x^2+4x)/(x^2+x-12)

x/(x-3)

200

Simplify

(3x-9)/(5x^2-14x-3)

3/(5x+1)

300

Simplify

(x^2-25)/(x^2+12x+35)

(x-5)/(x+7)

400

Simplify:

(x^2-13x+36)/(x^2-16)

(x-9)/(x+4)

500

(6x^2-x-40)/(4x^2+12x+5)

(3x-8)/(2x+1)

Multiplying...

100

Multiply:

(x^2-2x-3)/(x^2-x-2)*(x^2+x-6)/(x^2+2x-15)

(x+3)/(x+5)

200

(x^2-4x-5)/(x^2-3x+2)*(x^2-4)/(x^2-3x-10)

(x+1)/(x-1)

300

Multiply:

(x^2-2x-8)/(9x^2-16)*(3x^2+10x+8)/(x^2-16)

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

400

Multiply:

(4x^2+15x+9)/(8x^2+10x+3)*(2x+1)/(x^2+4x)

(x+3)/(x(x+4))

500

Multiply:

(4x^2-20x+25)/(x^2-4x)*(3x-12)/(2x-5)

(3(2x-5))/x

Add/Subtract

100

Add..

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

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

200

Subtract...

(2x)/(x-1)-9/(x-2)

(2x^2-13x+9)/((x-1)(x-2))

300

Add..

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

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

400

Subtract...

x/(x+3)-18/(x^2-9)

(x-6)/(x-3)

500

Add...

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

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

Solving Equations

100

(n+5)/(n+8)=1+6/(n+1)

n=-17/3

200

4/(n+1)+1/(n^2-5n+6)=1/(n-6)

n=8

300

3/(x-5)-20/(x^2-25)=2/(x+5)

No Solution

400

x/(x-6)+3/(x+8)=(x^2)/(x^2+2x-48)

x=18/11

500

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

x=1/2, x=-6

Random

100

Identify the vertical asymptote

f(x)=(x^2-x-6)/(4x-12)

VA:  

(x+2)/4

200

simplify (3x^2-12)/(x^2+4x+4)

(x-2)/(x+2)

300

If it takes Richard 45 mins to wash a car and it takes Bill 36 mins to wash the same car. How long would it take them working together to wash a car?

20 mins

400

If Harry can rake leaves twice is fast as Rachel and they can rake a yard together in 32 mins. Then how long would it take Rachel on her own to rake the yard?

96 mins

500

If Rob can vacuum 14 rooms in 40 mins and Jill can vacuum 12 rooms in 30 mins. How long would it take them to vacuum 20 rooms together?

26.7 mins