U10 Rational Expressions & Functions

Simplify/Multiply/Divide Expressions

100

(35p^3-56p^2+21p)/(21p^2+56p)

((p-1)(5p-3))/(3p+8)

0, -8/3

200

(8/(x^2-6x+8))*((-r^2+14r-40)/(8r-80))

(-1/(r-2))

r cannot equal 4, 2, 10

300

Divide and state excluded values.

(r^4+13r^3+44r^2+24r+70)/(r+7)

r^3+6r^2+2r+10

r cannot equal -7

400

(10v^2+32v-32)/(2v+8)div(5v^2-29v+20)/(v-8)

(v-8)/(v-5)

v cannot equal -4, 8, 5, 4/5

500

Divide and state excluded values

((10a^2-60a)/(a-5))/((a^2-3a-18)/(15+2a-a^2))

-10a

a cannot equal 6, 5, -3

Adding & Subtracting Rational Expressions

100

(a+2)/(6a^2+36a)+(a+4)/(3a^2+36a)

a cannot equal 0, -6

(a+3)/(3a(a+6)

200

(2x)/(6x)+(x+2y)/(2xy)

(2xy+3x+(6y))/(6xy)

x cannot equal 0, y cannot equal 0

300

3/(n+4)+(n-5)/(n-3)

(n^2+2n-29)/((n-3)(n+4))

n cannot equal 3, -4

400

(5/3)-((n+6)/(15n^2-6n))

(25n^2-11n-6)/((3n)(5n-2))

n cannot equal 0, 2/5

500

(n+4)/(n^2-2n-24)-(6/(3n))

(-n+12)/(n(n-6))

n cannot equal 6, 0, -4

Solving Rational Equations

100

5/x=7/(x+2)

x=5

200

1/n+1/3=1

n=1.5

300

((2r-2)/(r-5))+((r+1)/(r-5))=1

r=-2

400

After school, Chris completes his homework in 3 hours, and Erik completes his in 2 and a half hours. If they work together at MAC, how long will it take them to complete it?

t=1 and 4/11 hrs

500

(1/(x-2))-((x+4)/(x-2))=(4x^2+6x-18)/(x^2-2x)

x=-3, 6/5

Inverse/Direct Variation

100

Do the ordered pairs (2, 9) (3, 6) (0.5, 36) show a direct or inverse variation? What is the constant of variation?

Inverse, k=18

200

Write an equation to represent the relation (-1, 6) (-3, 18) (6, -36).

y=-6x

300

If y varies directly as x and y=-15 when x=5, find y when x=3.

y=-9

400

If y varies inversely as x and y=-6 when x=2, find y when x=-7

y=12/7

500

The time needed to travel a certain distance varies inversely with the rate of speed. If it takes 8 hours to travel a certain distance at 36 miles per hour, how long will it take to travel the same distance at 60 miles per hour?

4.8 hrs

Graphing Rational Functions

100

What are the asymptotes of 

y=5/x

x=0

y=0

200

What are the asymptotes of

y=3/(x-2)+10

x=2

y=10

300

Graph 

y=36/x

(1, 36) (2,18) (3, 12) (4,9) (6,6) (9,4) (12,3) (18,2)(36,1)

(-1, -36) (-2,-18) (-3, -12) (-4,-9) (-6,-6) (-9,-4) (-12,-3) (-18,-2)(-36,-1)

400

Graph the function

y=40/(x-2)

(3,40) (4,20) (6,10) (10,5) (12,4) (22,2) (42,1)

(-3,-40) (-4,-20) (-6,-10) (-10,-5) (-12,-4) (-22,-2) (-42,-1)

500

Graph the function

y=-20/(x-3)+2

(4,-18) (5,-8) (7,-3) (8,-2) (13,0) (23,1)

(2,22) (1,12) (-1,7) (-2,6) (-7,4) (-17,3)