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Algebra - Rational Expressions and Equations (21 Problems)

Rational Expressions and Equations (21 Problems)

Which numbers cannot be used in place of the variable in each
rational expression?

1.) 2y+1__
y^2-y-6

2.) a^2-b^2
a-b

Reduce each expression to lowest terms.

3.) 4x^2
2x^9

4.) -2x-8__
x^2+2x-8

Perform the indicated operation.

5.) 3 * 2a+2_
a^2+a 6

6.) -2a^2 * 20a__
3a^2 15a^3

7.) w^2-1 * _w-1___
(w-1)^2 w^2+2w+1

Build each rational expression into an equivalent rational
expression with the indicated denominator.

8.) -7yt = ?__
3x 18xyt

9.) 4 5x_
x-y' 2y-2x

Perform the indicated operation. Reduce each answer to lowest
terms.

10.) 4_ - 1_
9 9

11.) a+7_ + 9-5a_
a-4 a-4

12.) y _ + 2y
4

13.) 3 _ + 2_
x+1 x-1

14.) 2 + 3_
x-3 3-x

15.) 1 + 1_
9 3x__
x - 1_
9 x

Simplify each complex fraction.

16.) ab + b^2
4ab^5
a+b__
6a^2b^4

Solve each equation.

17.) x = 4_
3 x+1

Solve each equation. Watch for extraneous solutions.

18.) 5 = y+7 + 1
y-3 2y-6

19.) -3 = x__
x -3

Bonus Problems

20.) The golden ratio. The ancient Greeks thought that the
most pleasing shape for a rectangle was one for which the
ratio of the length to the width was approximately 8 to 5,
the golden ratio. If the length of a rectangular painting is
2 ft longer than its width, then for what dimensions would
the length and width have the golden ratio?

21.) Bear population. To estimate the size of the bear
population on the Keweenaw Peninsula, conservationists
captured, tagged, and released 50 bears. One year later, a
random sample of 100 bears included only 2 tagged bears.
What is the conservationist's estimate of the size of the
bear population?

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