ch 9 algebra II

add/subtract fractions

100

3/x + 5/y

(5x + 3y)/ xy

200

-7xy/3x + 4y²/2y

-y/3

300

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

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

400

3/(x+2) + (4x+5)/(3x+6)

(4x+14)/3(x+2)  or (4x + 14)/(3x + 6)

500

4/(4x² - 4x + 1) - 5x/(20x² - 5)

(-2x² + 9x + 4)/(2x+1)(2x-1)²

multiply/divide fractions

100

5ab³/25a²b²

b/5a

200

(x²-4)/(x-2)(x+1)

(x+2)/(x+1)

300

5r²/(r²-4) x (r+2)/10r⁵

1/2r³(r-2)

400

(x²-5x+4)/(2x-8) divided by (3x² - 3x)

1/(6x)

500

(a²-b²)/(4a) divided by (a+b)/(2a)

(a-b)/2

graphs/D & R, asymptotes

100

identify the asymptotes for f(x) = 1/(x - 1)

x = 1, f(x) = 0

200

Identify the asymptotes and the domain and range for f(x) = -3/(x-2) 

x = 2, f(x) = 0

D: {x| x cannot equal 2}

R: {f(x) | f(x) cannot equal 0}

300

Identify the asymptotes and the domain and range for f(x) = [1/(x + 1)]  - 5

x = -1

f(x) = -5

D: {x|x cannot equal -1}

R: {f(x) | f(x) cannot equal -5}

400

Graph the function and state the asymptotes, domain and range.

f(x) =[ 1/(x+4)] - 2

x = -4

f(x) = -2

D: {x|x cannot equal -4}

R: {f(x)|f(x) cannot equal -2}

See graph

500

Graph the function and state the asymptotes and domain and range.

f(x) = [-1/(x+5)] + 6

x = -5

f(x) = 6

D: {x|x cannot equal -5}

R: {f(x)|f(x) cannot equal 6}

See graph

Variations

100

If y varies inversely as x and y = 12 when x = 10, find y when x = 15.

y = 8

200

If y varies directly as x, and y = 39 when x = 52, find y when x = 22.

y = 16.5

300

If y varies jointly as x and z and y = 60 when x = 3 and z= 4, find y when x is 6 and z = 8.

y = 240

400

If y varies directly as z and inversely as x, and y = 10 and z = 5 when x = 12.5, find z when y = 37.5 and x = 2.

z=3

500

The area A of a trapezoid varies jointly as its height and the sum of its bases. If the area is 480 sq. meters when the height is 20 meters and the bases are 28 meters and 20 meters, what is the area of a trapezoid when it height is 8 meters and its bases are 10 meters and 15 meters?

A = 100 m²

Solving rational equations

100

x/(x-1) = 1/2

x = -1

200

2 = 4/n + 1/3

n = 12/5 or 2 2/5

300

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

x=-3

400

1/(n+3) + 5/(n²-9) = 2/(n-3)

n=-4

500

1/(w+2) + 1/(w-2) = 4/(w²-4)

no solution