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

- a = 5 x / 8, b = 5 x / 2, a / b
- a = 10, b = 4 x / 5, a / b
- a = 15 x^2 / (7 y^2), b = 9 x^3 y / (21 x y^3), a / b
- 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
- 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.
- 2 a / x + 3 b / x
- 3 b / (2 x) - 5 c / (4 x)
- 2 / (-x - 1) + 7 / (x + 1)

- (x + y) / 3 - (x - y) / 5
- 1 / (x + 1) + 2 / (x - 2)
- 5 / (x - 2) - (3 x + 4) / (x^3 - 8)
- 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.
- 2x/5 - x/3 = 2/15
- 1/3/x = 5/x + 1/2
- (3x - 116)/6 + (180 - 5x)/9 = 0
- (x - 1)/8 - (x + 1)/18 = 1
- 15x/4 = 9/4 - (3 - x)/2

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

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