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. p 2 + 10 p q + 25 q 2 p 2 + 6 p q + 5 q 2 ÷ 10 p + 50 q 2 p 2 − 2 q 2
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. p 2 + 10 p q + 25 q 2 p 2 + 6 p q + 5 q 2 ÷ 10 p + 50 q 2 p 2 − 2 q 2
Solution Summary: The author calculates the simplified form of the expression, p2+10pq+25q
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.
p
2
+
10
p
q
+
25
q
2
p
2
+
6
p
q
+
5
q
2
÷
10
p
+
50
q
2
p
2
−
2
q
2
Please help me with these questions. I am having a hard time understanding what to do. Thank you
Answers
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Q.1) Classify the following statements as a true or false statements:
a. If M is a module, then every proper submodule of M is contained in a maximal
submodule of M.
b. The sum of a finite family of small submodules of a module M is small in M.
c. Zz is directly indecomposable.
d. An epimorphism a: M→ N is called solit iff Ker(a) is a direct summand in M.
e. The Z-module has two composition series.
Z
6Z
f. Zz does not have a composition series.
g. Any finitely generated module is a free module.
h. If O→A MW→ 0 is short exact sequence then f is epimorphism.
i. If f is a homomorphism then f-1 is also a homomorphism.
Maximal C≤A if and only if is simple.
Sup
Q.4) Give an example and explain your claim in each case:
Monomorphism not split.
b) A finite free module.
c) Semisimple module.
d) A small submodule A of a module N and a homomorphism op: MN, but
(A) is not small in M.
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