Rational Equations
Solving Equations
Simplify/Factoring
Miscellaneous 1
Miscellaneous 2
100
Given the function. What value(s) of x is the function undefined/discontinuity?
f(x)=(3x)/(x^2+4x-5)
A. x = 0, 1, -5 B. x = 0
C. x = 2, 3 D. x = 1, -5
Answer: D
100
Solve:
Round to the nearest hundredth.
3^(2x+3)=(sqrt3)^(x+4)
x=-0.67
100
Factor
x^3-5x^2+3x-15
(x^2+3)(x-5)
100
What is the largest real number solution to the polynomial:
p(x) = (x-5)(3x+5)(x^2-7x+15)
x=5
100
A function is shown
f(x) = (x+2)/(x^2-3x-10)
At what positive x value does the function have a discontinuity?
Ans. x = 5
200
Solve:
1/(x-8)-1=7/(x-8)
x=2
200
Solve for x:
Round to nearest thousandth
3*2^(7x)=48
x=0.571
200
Factor
x^3+2x^2-9x-18
(x+2)(x+3)(x-3)
200
Nancy can paint a fence in 3hrs. It takes Ben 4hrs to do the same job. If they work together, how many hours should it take?
1.7 hours
200
What is the solution to the equation?
(x^2+5x-14)/(x-2)=-21
x=-28
300
Given 6/r+4/(r-4)=1
a) What two values of r are undefined?
b) Solution(s)?
a) r is undefined at 0 and 4
b) r = 2, 12
300
Solve for x:
log_2(2x-5)=5
x = 18.5
300
Factor
x^3-x^2-6x
x(x-3)(x+2)
300
If f(x) = 2x2-7x and g(x) = 10-x. What is h(x) when
h(x) = 4f(x) -g(x)
h(x)=8x^2-27x-10
300
A polynomial eq. with real coefficients has roots at x=2±√(3), x=2i and x = -1(Multiplicity(3)) What is the minimum degree of the polynomial equation?
7 roots
400
Given the equation:
2/(x-1)=4/(x+1)-2/(x+3)
a) What are the restrictions on x?
b) Solutions?
a) x = -1, -3, 1
b) No Solution
400
Given
f(x)=3Absx-1 and g(x)=0.03x^3-x+1
find when f(x)=g(x)
X= -0.986, 0.501 and 11.288
400
Simplify by factoring
(x^3-2x^2-9x-18)/(x^3-x^2-6x)
(x+3)/x
200 - BONUS: What value of x does the expression have a discontinuity?
x=?
400
Find the x coordinate of the center of the circle
4x^2+4y^2-4x+2y-1=0
x=1/2
400
What is the center and radius of the circle?
(x-4)^2+(y+6)^2=16
Center: (4,-6)
Radius : sqrt16 =4
500
Solve
x/(2x+2)=(-2x)/(4x+4)+(2x-3)/(x+1)
x=3
500
What is the solution to
8(2^(x+3))=48
A. x = log2(3)
B. x = 3 - log2(6)
C. x = -3 + log2(6)
Answer: C
500
The expression (x+4) is a factor of x2+kx-20. What is the value of K?
K =-1
500
Given the interval (4,10], list the following functions from least to greatest.
f(x) = 2^x
g(x) = 2x
h(x) = x^2
g(x), h(x), f(x)
500
Given the graph, what is f(x) in factored form?
f(x)=(x+3)(x-2)^2(x-5)