Operations With Rational Expressions

Inverse Variation and Graphing Rational Funct.

100

determine if the relationship between these variables is a direct variation, inverse variation or neither x. y. 0.2 8 0.5 20 1.0 40 1.5 60

direct

200

Given the variable relationship below, what is the value of Y when X=10 x y 3 16 4 12 6 8 8 6 12 4 16 3

When x=10, y=4.8

300

Suppose x and y vary inversely, and x=8 when y=7. What is the function that models the inverse variation?

y= -56/x

400

Write an equation for the translation of y= 2/x given the asymptotes: x=-2 and y=3

y= 2/(x+2) +3

500

Identify the x or y intercepts, the asymptotes, and domain and range of the equation: y= 15/x

x or y intercepts: none asymptotes: horizontal: y=0 vertical: x=0 domain: all real numbers, except x=0 range: all real numbers, except y=0

Rational Functions and Their Graphs

100

Find the points of discontinuity (x+5)/(x²+9x+20)

PODS= x=-5 and x=-4

200

Find the vertical asymptote y= (x-3)/(x+5)

VA= x=-5

300

What quadrant(s) are the graph of this function y= (3x)/(x-4)

1 and 3

400

Find the vertical asymptote y= 3/(x+2)

VA= x=-2

500

Find the horizontal asymptote y= 5/(x+6)

HA= y=0

Rational Expressions

100

Simplify the expression and state any restrictions on the variables (2x)/(4x²-2x)

1/(2x-1) ; x cannot equal 0 or 1/2

200

Simplfy and state any restrictions (49-z²)/(z+7)

7-z; x cannot equal -7

300

Multiply and state any restrictions (2x⁴)/(10y^-2) x (5y³)/(4x³)

(xy^5)/4; x and y cannot equal 0

400

Multiply and state any restrictions (2x+12)/(3x-9) x (6-2x)/(3x+8)

-4(x+6)/3(3x+8); x cannot equal 3 or -8/3

500

Divide and state any restrictions (3x³)/(5y²) divided by (6y^-3)/(5x⁵)

y/(2x^2); x and y cannot be equal to 0

Adding and Subtracting Rational Expresion

100

Simplify (x+1)/(x-1) + -2/(x²-x)

2(x+2)(x-3)

200

Simplify x/x²-4) + 1/(x+2)

(x-1)(x-2)^2 (x+4)

300

What is a complex fraction?

A rational expression that has at least 1 fraction in its numerator or denominator or both.

400

What is the LCD of 1/x, x/y, and 1/y?

xy

500

Simplify (1/xy - 1/y²)/(1/x²y - 1/xy²)

x

Solving Rational Equations

100

Is this a rational equation? x+1/2=3/4

no

200

Solve 3/x=5

6

300

Solve 1/(b+1) + 1/(b-1)= 2/(b²-1)

No Solution

400

What are the solutions of the rational equation? x/(x-3) + x/(x+3) = 2/(x²-9)

x= -1, 1

500

What is the LDC of (x-1)/(x²+3x+2) + (2x)/(x+2)= (x-1)/(x+1)

(x+2)(x+1)