We have learned how to simplify, add, subtract, multiply, and divide rational expressions. The procedure for each operation is different, and it takes considerable practice to determine the correct method to apply for a given problem. The following review exercises give you the opportunity to practice the specific techniques for simplifying rational expressions. For Exercises 1–20, perform any indicated operations, and simplify the expression. a a 2 − 9 − 3 6 a − 18
We have learned how to simplify, add, subtract, multiply, and divide rational expressions. The procedure for each operation is different, and it takes considerable practice to determine the correct method to apply for a given problem. The following review exercises give you the opportunity to practice the specific techniques for simplifying rational expressions. For Exercises 1–20, perform any indicated operations, and simplify the expression. a a 2 − 9 − 3 6 a − 18
Solution Summary: The author explains how to factor the denominator of the rational expressions.
We have learned how to simplify, add, subtract, multiply, and divide rational expressions. The procedure for each operation is different, and it takes considerable practice to determine the correct method to apply for a given problem. The following review exercises give you the opportunity to practice the specific techniques for simplifying rational expressions.
For Exercises 1–20, perform any indicated operations, and simplify the expression.
(1) Let M and N be non-empty subsets of a linear space X, show that whether
= U or not, and show that there whether exsits a liear function
from P₂(x) into R' which onto but not one-to-one or not.
ام
(2) Let R be a field of real numbers and P,(x)=(a+bx+cx? / a,b,ce R} be a vector space
over R, show that whether there exsit two hyperspaces A and B such that AUB is a
hyperspace or not.
(3) Let A be an affine set in a linear space X over afield F and tEA, show that A-t is a
subspace of Xand show that if M and N are balanced sets then M+N is balanced set.
(4) Write the definition of bounded set in a normed space, and write with prove
an equivalent statement to definition.
(5) Let d be a metric on a linear space X over a field F, write conditions on d in order to
get that there is a norm on X induced dy d and prove that.
(6) Let M be a non-empty subset of a normed space X, show that xEcl(M) iff for any r>o
there exsits yEM such that llx-yll
Find all solutions to the following equation. Do you get any extraneous solutions? Explain why or why
not.
2
2
+
x+1x-1
x21
Show all steps in your process. Be sure to state your claim, provide your evidence, and provide your
reasoning before submitting.
Directions: For problems 1 through 3, read each question carefully and be sure to show all work.
1. What is the phase shift for y = 2sin(2x-)?
2. What is the amplitude of y = 7cos(2x+л)?
3. What is the period of y = sin(3x-π)?
Directions: For problems 4 and 5, you were to compare and contrast the two functions in each problem situation. Be sure to
include a discussion of similarities and differences for the periods, amplitudes, y-minimums, y-maximums, and any phase shift
between the two graphs. Write in complete sentences.
4. y 3sin(2x) and y = 3cos(2x)
5. y 4sin(2x) and y = cos(3x- -플)
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