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Undefined

100

For what values of x is the expression undefined?

1/x

the expression is undefined for x=0

so x cannot equal 0

200

For what values of w is the expression undefined?

3w³/(5w-7)

the expression is undefined for w=7/5

so w cannot equal 7/5

300

For what values of x is the expression undefined?

(2x+3)/(x²+3x-4)

the expression is undefined for x=-4 and 1

so x cannot equal -4 or 1

400

For what values of x is the expression undefined?

(x-6)/(x²+7)

the expression is never undefined

Simplify

100

Simplify the following expression:

2x²/4x

x/2

200

Simplify the following expression:

(3y+21)/(4y+28)

3/4

300

Simplify the following expression:

(x²-6x+9)/(x²-9)

(x-3)/(x+3)

400

Simplify the following expression:

(x²+3x+2)/(x²+5x+4)

(x+2)/(x+4)

Solve

100

Solve the equation:

(x+2)/x = 4/7

x=-14/3

200

Solve the equation:

12/(x²-9) - 2/(x-3) = 7/(x+3)

x=3

300

Solve the equation:

3/(y-1) - 1/4 = 5/(y+1)

y=-11 and y=3

400

Solve the equation for m:

N = b/(t+m)

m = b/N - t

d=r*t / Word

100

The winner of a 500 mile car race drove an average of 96.5 mph. What was the winners time?

t = 5.18 hours

OR 

the winners time was roughly 5 hours and 10 min

200

In a certain fraction the denominator is 4 less than the numerator. If 3 is added to both the numerator and denominator, the resulting fraction is equal to 3/2. What was the original fraction? 

The original fraction is 26/21

300

The speed of the streams current is 4 mph. A boat travels 7 miles upstream in the same time that it takes to travel 15 miles downstream. What is the speed of the boat in still water? 

The speed of the boat is 11mph. 

400

An experienced shipping clerk can fill an order in 12 hours. The new clerk takes 13 hours to fill the same job. How long will it take to fill the order if they work together?

When they work together they can fill the order in 6.24 hours. 

add/sub & mult/div

100

Add the two expressions and simplify:

a²/(a+4) + (a-12)/(a+4)

(a-3)

200

Multiply the two expressions and simplify:

(5x+5)/(3x-6) * (2x-4)/(x+1)

10/3

300

Subtract the two expressions and simplify:

7/(3p²) - 5/p

(7-15p)/(3p²)

400

Divide the two expressions and simplify:

(x+7)/(x²+x-12) / (x-5)/(x²+2x-8)

(x+7)(x-2) / (x-3)(x-5)

OR

(x²+5x-14)/(x²-8x+15)