Simplifying Rational Expressions
Solving Rational Functions
Graphing Rational Functions
Be Rational!
Radical,dude!
100
Add the expressions and simplify.
12/(5x)+7/(6x)
107/(30x)
100
Solve the equation.
5/x=7/(x+2)
x=5
100
What is the equation of the vertical asymptote?
f(x)=1/(x-3) +2
x=3
100
Multiply and simplify:
(6x^2-18x)/(x^2-10x+21) * (x^2-14x+49)/(3x^2)
(2(x-7))/x
100
Find the Least Common Multiple (LCM):
10x^2-15x
5x^3
5x^2(2x-3)
200
Simplify the rational expression.
(x^2+5x-14)/(x^2-4x+4)
(x+7)/(x-2)
200
Solve the equation.
(x+12)/3=(2x+3)/(x+2)
x= -5, -3
200
Determine all x-intercepts and holes:
f(x)= (x^2 -9)/(x^2 -x -12)
x-intercepts: x=3
Holes: x=-3
200
Add the expressions and simplify.
x/(x^2-x-12) + 5/(12x-48)
(17x+15)/(12(x-4)(x+3)
200
Simplify:
3√(16x11)
2x3* 3√2x2
300
Simplify the rational expression.
(x^2-9x+14)/(x^2-5x-14)
(x-2)/(x+2)
300
Solve the equation.
1/(x+6)+(x+1)/x=13/(x+6)
x=2,3
300
Identify the horizontal asymptote of the function:
f(x) = 3x3 + 12x2 - 16
5x3 -125
y = 3/5
-or-
y = 0.6
300
Multiply and simplify.
(x-3)/(2x-8) * (6x^2-96)/(x^2-9)
(3(x+4))/(x+3)
300
Define the domain and range for the function:
f(x) = 2√(x + 7)
Domain: x > -7
Range: y > 0
400
Simplify: write your answer in radical form.
(ab1/2)3
a1/2b
a2*√ab
400
Solve the equation.
(3x)/(x+1)+6/(2x)=7/x
x=-2/3, 2
400
f(x)=3/(x-1)-2
a) Graph the function.
b) State the domain and range.
domain:
x!=1
range:
y!=-2
400
Subtract the expressions and simplify.
(x^2-5)/(x^2+5x-14) - (x+3)/(x+7)
(-x+1)/((x+7)(x-2)
400
Surprise! Radical Problem:
Simplify:
3√(16x5y2)
2x2 * 3√(2x2y2)
500
Simplify the rational expression.
(8x^2+10x-3)/(6x^2+13x+6)
(4x-1)/(3x+2)
500
4/(n+1)+1/(n^2-5n-6)=1/(n-6)
What is 8?
500
a) Identify the transformation of the parent function.
b) Graph the function.
f(x)=3/(x+8)-3
Vertical stretch by a factor of 3.
Translation left 8, and down 3.
500
Divide and simplify.
(3x+27)/(6x-48) div (x^2+9x)/(x^2-4x-32)
(x+4)/(2x)
500
Solve; check for extraneous solutions.
2 + √(x - 5) = √(x + 3)
x = 6