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.
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Unit Test
Unit Test Review Active
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Which statement is true about the graph of the equation y = csc¯¹(x)?
There is a horizontal asymptote at y = 0.
उद
There is a horizontal asymptote at y = 2.
There is a vertical asymptote at x = 0.
O There is a vertical asymptote at x=-
R
Mark this and return
C
Save and Exit
emi
ے ملزمة احمد
Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to-
one iff (f(x1),f(x2),...,f(x) } linearly independent.
(b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a
hyperplane of X.
مبر خد احمد
Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is
convex set or not, affine set or not.
Write with prove an
application of Hahn-Banach theorem.
Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)
Let M be a proper subspace of a finite dimension vector space X over a field F show that
whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M
or not.
(b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L
prove convex subset of X and hyperspace of X.
Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and
A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that
gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA.
(b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there
Xiff there
exists fE X/10) and tE F such that M=(xE X/ f(x)=t).
(c) Show that the relation equivalent is an equivalence relation on set of norms on a space
X.
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