Operations With Rational Expressions

Horizontal Asymptotes

100

Find the HA for y= 2/x 

y=0

200

Find the HA for 2x/(x-3)

y=2

300

Find the HA for y=(3x²-10x+4)/(2x-7)

No HA

400

Find the HA for y=(8x⁴-3x+7)/(2x⁴+12)

y=4

500

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

y=0

Vertical Asymptotes

100

Find the vertical asymptotes (x+5)/(x²+9x+20)

x=-4

200

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

VA= x=-5

300

Find the vertical asymptotes for y= (3x)/(x²-4)

x=2 and x=-2

400

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

VA= x=-2

500

Find the vertical asymptote y= (x²+10x-80)/(x²-11x+24)

x=3

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

xy

400

Subtract: (6x-7)/(x²+6x+5) - 4/(x+5)

(2x-11)/(x+5)(x-1)

500

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

x

Solving Rational Equations

100

Solve 3/x=5

6

200

Solve: 5/(x²-3x+2) - 1/(x-2) = 1/(3x-3)

x=5

300

Solve 1/(b+1) + 1/(b-1)= 2/(b²-1)

No Solution

400

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

(x+2)(x+1)

500

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

x= -1, 1