SOLUTION: Hi I'm trying to work out with the exercises in my txtbook..COuld you please help me solve these problems: page 449 Question 16 Find all the numbers for which each rational exp

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Question 187020This question is from textbook Introductory and Intermediate Algebra
: Hi I'm trying to work out with the exercises in my txtbook..COuld you please help me solve these problems:
page 449 Question 16
Find all the numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state.
(y+8)/ 16y^2-y-2
page 457 Question 50
Divide as indicated.
(x^2+x)/(x^2-4) divided by (x^2-1)/(x^2+5x+6)
Thanks in Advance
Kattie This question is from textbook Introductory and Intermediate Algebra

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Find all the numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state.
(y+8)/ 16y^2-y-2
Solve 16y^2-y-2 = 0
y = [1 +- sqrt(1 - 4*16*-2)]/32
y = [1 +- sqrt(129)]/32
y = [1 + sqrt(129)]/32 or y = [1 - sqrt(129)]/32
These are the values of y for which the expression is not defined.
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page 457 Question 50
Divide as indicated.
(x^2+x)/(x^2-4) divided by (x^2-1)/(x^2+5x+6)
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Factor where you can to get:
[x(x+1) / (x+2)(x-2)] divided by [(x-1)(x+1)/(x+2)(x+3)]
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Invert the denominator and multiply:
[x(x+1) / (x+2)(x-2)] multiplied by [(x+2)(x+3)/(x-1)(x+1))]
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Cancel any factors that are common to a numerator and a denominator
such as (x+1), (x+2)
[x / (x-2)] multiplied by [(x+3)/(x-1)]
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Simplify:
[x(x+3)] / [(x-2)(x-1)]
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Cheers,
Stan H.