Test 3

rational expressions

100

f(x)= (9-x²)/(x²-2x-3)

domain:

x!=3 x<!=-1

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

200

(6x+6)/(2x+4)*(x+2)/(6x²-6)

1/(2(x-1))

300

(x+3)/9x² -: (x²+6x+9)/5x⁴

5x²/9(x+3)

400

7/(y²+5y+4) + 3/(y²+y)

(2(5y+6))/(y(y+1)(y+4))

500

x/(5x²-10x) - (x-8)/(x-2)

(-(5x+39))/(5(x-2))

simplify complex fractions or long division

100

(3y^-1+z^-1)/(y^-2z^-2)

yz(3z+y)

200

(4y/x²)/(3z/5xy)

(20y²)/(3xz)

300

(6x³+10x²-13x+8)/(3x-1)

2x²+4x-3+ 5/(3x-1)

400

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

2y+x

500

(8w³-4w²-10w+3)-:(2w-1)

4w²-5+ (-2)/(2w-1)

shared work or simplifying radical expressions

100

5/(a-3)=-8/(a-6)

a=54/13

200

5/(3x+6)=1/(x²-4)

x=13/5

300

(x²+1)/(2x²-7x-15)-2/(x-5)=5/(2x+3)

x=4

400

A swimming pool can be filled in 8 hours if water enters through a pipe alone, or 20 hours if water enters through a hose alone. If water is entering through both a pipe and a hose, how long will it take to fill the pool?

It will take about 5.71 hours to fill the pool with both the pipe and the hose.

500

Samuel can wax his car three times as fast as Daniel. When they work together, they can wax the car in 2 hours. How long would it take Daniel, working alone, to wax the car?

It would take Samuel about 2.67 hours to wax the car by himself. It would take Daniel 8 hours.

simplify the radical or algebraic expression

100

sqrt(54w⁷z¹⁴)

3w³z⁷sqrt(6w)

200

sqrt(45w⁵z⁸)

3w²z⁴sqrt(5w)

300

(8x⁶y^-12)^-2/3

y⁸/4x⁴

400

((y^-5/6z^3/16)⁴)/z^1/20

z^7/10/y^10/3

500

(-b^1/2b^3/4)/b^-5/2

-b^15/4

multiply conjugates or rationalize denominators

100

(sqrt(5)-3)(2sqrt(5)+7)

-11+sqrt(5)

200

(5sqrt(2)-3)(5sqrt(2)+3)

41

300

root(3)(2x/50x⁴y)

(root(3)(5y²))/5xy

400

root(3)(3x/6x⁴y²)

(root(3)(4y))/2y

500

(sqrt(x⁵y¹¹))/sqrt(xy)

x²y⁵