Mathematics

Find the domain of the rational function.

g(x) = fraction numerator 4 minus 3 x over denominator 2 end fraction


{x|x is a real number, x ≠bevelled 3 over 4 }

{x|x is a real number, x ≠ 2}

{x|x is a real number}

{x|x is a real number, x ≠ bevelled 3 over 4, x ≠ 2}

——————————–

Find the domain of the rational function.

R(x) = fraction numerator 3 plus 2 x over denominator x cubed plus x squared minus 2 x end fraction


{x|x is a real number, x ≠ 0, x ≠ 1, x ≠ -2}

{x|x is a real number, x ≠ 0, x ≠ 1, x ≠ -2, x ≠ minus bevelled 2 over 3}

{x|x is a real number, x ≠ 1, x ≠ -2}

{x|x is a real number}

————————————–

Simplify the expression.

fraction numerator 4 b squared minus 16 over denominator b plus 2 end fraction


4(b – 2)

4(b + 2)

2(b – 8)

fraction numerator 2 left parenthesis b squared minus 4 right parenthesis over denominator b end fraction

——————————————

Simplify the expression.

fraction numerator p squared minus 8 p plus 15 over denominator p squared minus 6 p plus 9 end fraction


fraction numerator p squared minus 8 p minus 15 over denominator p squared minus 6 p plus 9 end fraction

p-5

fraction numerator p minus 5 over denominator p minus 3 end fraction

fraction numerator p minus 5 over denominator p plus 3 end fraction

——————————————-

Multiply the rational expressions and simplify.

fraction numerator 3 x squared plus 2 x minus 1 over denominator 4 x minus 2 end fraction cross times fraction numerator 3 x minus 2 over denominator 2 x squared plus x minus 1 end fraction


fraction numerator 9 x squared minus 9 x plus 2 over denominator 8 x squared minus 8 x plus 2 end fraction

fraction numerator 9 x plus 2 over denominator 8 x plus 1 end fraction

9 x squared minus 9 x space plus space 2

fraction numerator 3 x cubed space plus space 5 squared plus x space minus 1 over denominator 6 x minus 4 end fraction_x000D_

————————————————

Divide the rational expressions and simplify.

fraction numerator x minus 4 over denominator 2 x minus 1 end fraction divided by fraction numerator x squared minus 16 over denominator 2 x minus 1 end fraction


fraction numerator 1 over denominator x plus 4 end fraction_x000D_

x minus 4

fraction numerator x cubed minus 4 x squared minus 16 x space plus space 16 over denominator 4 x squared minus 4 x space plus space 1 end fraction

fraction numerator 1 over denominator x minus 4 end fraction

—————————————

Multiply the rational expressions and simplify.

fraction numerator 18 a space minus space 12 a squared over denominator 4 a squared plus 4 a space plus space 1 end fraction cross times fraction numerator 4 a squared plus 8 a space plus space 3 over denominator 4 a squared minus space 9 end fraction


fraction numerator 6 a over denominator 2 a plus 1 end fraction

minus fraction numerator 6 a over denominator 2 a plus 1 end fraction

fraction numerator 6 a left parenthesis 3 minus 2 a right parenthesis over denominator left parenthesis 2 a plus 1 right parenthesis left parenthesis 2 a minus 3 right parenthesis end fraction

-3

————————————————

Divide the rational expression and simplify.

fraction numerator x squared minus 4 over denominator 3 x plus 6 end fraction divided by fraction numerator 2 x squared minus 8 x plus 8 over denominator x squared plus 4 x plus 4 end fraction


fraction numerator left parenthesis x plus 2 right parenthesis left parenthesis x plus 2 right parenthesis over denominator 6 left parenthesis x minus 2 right parenthesis end fraction

minus fraction numerator x plus 2 over denominator 6 end fraction

fraction numerator 1 over denominator 6 left parenthesis x minus 2 right parenthesis end fraction

minus fraction numerator 2 left parenthesis x minus 2 right parenthesis left parenthesis x minus 2 right parenthesis over denominator 3 end fraction

—————————————————–

Find g(-2) for the function below.

g(x) = fraction numerator x squared plus 8 over denominator x cubed minus 25 x end fraction


2/21

2/7

6/29

-6/29

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The total revenue from the sale of a popular book is approximated by the rational function R(x) = fraction numerator 1000 x squared over denominator x squared plus 4 end fraction, where x is the number of years since publication and R(x) is the total revenue in millions of dollars. Find the total revenue at the end of the second year. Round to the nearest million dollars, if necessary.


$250 million dollars

$200 million dollars

$692 million dollars

$500 million dollars

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