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Name____________________________________________ Algebra 2 & Trig – Review 1.2 – Rational Expressions 1 −1 x is equivalent to 1. Expressed in simplest form, 1 x− x

1.

–1

2.

1 x +1 1 4. x −1

3.

1 x +1

3. Written in simplest form, the expression equivalent to (1) - 1

(2)

1 3 + xy

x2y2 − 9 is 3 − xy

(3) −(3 + xy) (4) 3 + xy

x 2 − 3x x 3 − x 2 −12x 5. The product of 2 and is x −9 x3 − 4x2 1 x−4 x2 (1) 1 (2) (3) (4) x2 3 (x − 3)(x − 4) 7. Find the solution set of

12 −2=2 x

9. Express in simplest form:

11. Solve:

x 2 − 6x 36 − x 2 ÷ x 2 + 8x + 12 x −2

3x − 4 4 x − 3 < 8 4

13. The length of a rectangle is

15. Simplify:

1 1 − a b

2. What is the sum of

(1) 1

3 x and ? x−3 3− x

(2) - 1

(3)

x+3 x−3

(4) 0

4. The solution set for the equation x +1 1 + = x − 2 is x −1 x −1 (1) {0}

(2) {2}

(3) {0,4}

(4) {4}

x2 − 9 6. For what value(s) of x is undefined? x−7 (1) 9 only

(2) 7 only (3) ±3

8. Reduce

6x 2 − 5x − 4 to lowest terms 8 − 2x − 3x 2

10. Solve and graph on number line:

(4) ±3 and 7

a a > +6 4 2

12. Express in simplest form: 4 x 2 −100 20 − 4 x 2x + 6 • 2 ÷ 2 2 x + 6x + 5 x + x − 6 2x − 9x + 10 2x + 4 and its width is x2 − 9

3 . Express the perimeter of the rectangle as a x−3 single fraction in simplest form. a b

Date_____________________

14. Express as a single fraction in simplest form: 18 y − 2 y −3 y −9

3x 16. Simplify x + 3 x 2 x −9


1 x 17. Simplify: 1 1+ x x−

18. Solve for x:

2 4 +5= x 3x

2 3x + 1 + =2 2x + 1 x + 2

19. Solve for x:

x 2 50 − = 2 x − 5 x + 5 x − 25

20. Solve for x:

21. Solve for x:

x −1 x − 2 = x + 3 x +1

22. Solve: x − 8 +

23. Solve: 3 −

2 <5 a +1

24. Simplify:

a −1 25.The expression b is equivalent to a +1 b 1 1 a−b a+b (1) (2) (3) (4) a−b a+b a+b a−b

27. Find the positive root of

1 x+2 = , x ≠1 4 x −1

29. Combine and simplify:

4 3 − 2 x − 25 x + 5

5 6 + y y2 31. Simplify: 3 1− y 33. Which fraction is defined for all real numbers? 1−

x 2 −1 (2) (1) x +1

x 2 −1 x 2 −1 x 2 −1 (3) (4) 2 2 x2 x +1 (x −1)

26. Express

15 =0 x

2x 2 − 5x + 2 9x 2 ⋅ 6x − 3 3x 2 − 6x

x 3 + 3x 2 − 4 x −12 in simplest form x 2 + 2x

28. For what value(s) of x is

4 x 2 − 3x + 2 undefined? x 3 − x 2 − 20x

30. The area of a rectangle is 3x 2 + 2x − 21. The length of the rectangle is x + 3. Write an expression in terms of x representing the width of the rectangle.

32. Simplify

x 2 − 25 x 2 + 8x + 12 x 2 + 7x + 10 ⋅ ÷ 2x + 12 4 x − 20 8x

34. For what value(s) of x is

2x undefined? x −5


Unit 2 - Review