### Chapter 11 - Algebra Coach Exercises

Algebra Coach Exercise on simplifying algebraic fractions.
For each question simplify the algebraic fraction. To do this drag-and-drop each question into the Algebra Coach and then click the Simplify button twice.

Required options setting: the negative exponent option should be set to the default, show as fraction setting, shown here: 1. (x^2 + 3 x) / (x^2 - 9 x)
2. (x^2 + 3 x) / (x + 3)
3. (2 x^2 + 6 x) / (5 x + 15)
4. (2 x^2 - 6 x) / (-5 x + 15)
5. (x^2 + 3 x - 10) / (x + 5)
6. (4 x - 6) / (2 x^2 + 7 x - 15)

Algebra Coach Exercise on multiplication and division of algebraic fractions.
Multiply or divide the following algebraic fractions, as indicated. To do this drag-and-drop each problem into the Algebra Coach. Then click the Substitute button and then click the Simplify button repeatedly.
1. a = 5 x / 8,   b = 4 / 5,   a * b
2. a = 10,   b = 4 x / 5,   a * b
3. a = 15 x^2 / (7 y^2),   b = 21 x^3 y / (9 x y^3),   a * b
4. a = 3 x y z / (4 x^2 y^2 z^2),   b = 8 x^3 y^2 z^2 / (9 x^2 y z),   a * b
5. a = (x + y) / (x - y),   b = (x^2 - y^2) / (x + y)^2,   a * b

6. a = 5 x / 8,   b = 5 x / 2,   a / b
7. a = 10,   b = 4 x / 5,   a / b
8. a = 15 x^2 / (7 y^2),   b = 9 x^3 y / (21 x y^3),   a / b
9. a = 4 x y z / (3 x^2 y^2 z^2),   b = 8 x y^2 z^2 / (9 x^2 y z),   a / b
10. a = (x + y) / (x - y),   b = (x^2 - y^2) / (x - y)^2,   a / b

Algebra Coach Exercise on addition and subtraction of algebraic fractions.
Add or subtract the following algebraic fractions, as indicated. To do this drag-and-drop each problem into the Algebra Coach and then click the Add Fractions button. In questions 4 to 7 click the Distribute button afterwards to distribute the numerator.
1. 2 a / x + 3 b / x
2. 3 b / (2 x) - 5 c / (4 x)
3. 2 / (-x - 1) + 7 / (x + 1)

4. (x + y) / 3 - (x - y) / 5
5. 1 / (x + 1) + 2 / (x - 2)
6. 5 / (x - 2) - (3 x + 4) / (x^3 - 8)
7. x / (x^2 - 4) + x / (x + 2)

Algebra Coach Exercise on fractional equations.
Solve each of the following fractional equations for x. To do this drag-and-drop each of them into the Algebra Coach and click the AutoSolve button.
1. 2x/5 - x/3 = 2/15
2. 1/3/x = 5/x + 1/2
3. (3x - 116)/6 + (180 - 5x)/9 = 0
4. (x - 1)/8 - (x + 1)/18 = 1
5. 15x/4 = 9/4 - (3 - x)/2

6. 2/3/x + 6 = 5
7. 4 + 1/(x + 3) = 8
8. (8x + 7)/(5x + 4) = - 2x/(5x + 1) + 2
9. 3/(x - 3) = 4/(x + 1) + 2/(x^2 - 2x - 3)
10. (x - 3)/(x + 2) = (x + 4)/(x - 5)

11. 9/(x^2 + x - 2) = 7/(x - 1) - 3/(x + 2)
12. 4/(x^2 - 1) + 1/(x - 1) + 1/(x + 1) = 0
13. 3/(x + 1) - (x + 1)/(x - 1) = x^2/(1 - x^2)
14. (9x + 20)/36 - x/4 = (4x - 12)/(5x - 4)
15. (6x + 7)/10 - (3x + 1)/5 = (x - 1)/(3x - 4)