Reteaching - RoweMathWiki
Name
Class
Date
Reteaching
11-5 Solving Rational Equations Solving rational equations uses the properties of simplifying rational expressions in an equation that solves for an unknown variable.
What is the the solution of
2 3 1 ? x 2x 4
2 3 1 ? x 2x 4
Solve
The denominators are x, 2x, and 4. The LCD is 4x.
2 3 1 4x 4x x 2x 4
2 3 1 4x 4x 4x x 2x 4
Multiply each side by 4x.
Distributive Property Simplify.
8+6= x
Add.
14 = x
Check your solution. For some rational equations, you may have to solve a quadratic equation after multiplying each side of the equation by the LCD. There may be more than one solution.
What is the the solution of 2
2 4 ? x x2
2 4 x2 2 x2 2 x x
Solve
2 4 x 2 (2) x 2 x 2 2 x x
2x2 + 2x = 4 x2 + x = 2 x2 + x 2 = 0 (x + 2)(x 1) = 0 x+2=0
x1=0
x = 2 or
x=1
Multiply each side by the LCD, x2.
Distributive Property Simplify. Divide each side by 2. Collect terms on one side. Factor the quadratic expression. Zero-Product Property Solve for x.
Check your solutions.
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
49
Name
Class
Date
Reteaching (continued)
11-5
Solving Rational Equations
Exercises Solve each equation. Check your solutions. 1.
1 2 3 x x
2.
4 6 10 2x 2x
3.
6 5 9 9b 3b
4.
1 5 8 20c 4c
6.
4 6 2 y y2
8.
2 4 2 z 1 z 1
5. 1
2 –1 x x2
7. 2 x 1
1 x2
9. Your sister can paint a room in 5 hours. Your dad can paint the same room in
1 hours. How long will it take your sister and your dad to paint the room if 2 they work together? 3
Solve each equation. Check your solutions. If there is no solution, write no solution.
10.
8 4 x 1 x 1
11.
6 2 x x 12 x 4
12.
5 1 2 – 12 4 x 3x
13.
4x 1 6 x x2 x–2
14.
5 1 5 x 7x 4 x
15.
6 4x 1 9( x 6) x6
2
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
50
Class
Date
Reteaching
11-5 Solving Rational Equations Solving rational equations uses the properties of simplifying rational expressions in an equation that solves for an unknown variable.
What is the the solution of
2 3 1 ? x 2x 4
2 3 1 ? x 2x 4
Solve
The denominators are x, 2x, and 4. The LCD is 4x.
2 3 1 4x 4x x 2x 4
2 3 1 4x 4x 4x x 2x 4
Multiply each side by 4x.
Distributive Property Simplify.
8+6= x
Add.
14 = x
Check your solution. For some rational equations, you may have to solve a quadratic equation after multiplying each side of the equation by the LCD. There may be more than one solution.
What is the the solution of 2
2 4 ? x x2
2 4 x2 2 x2 2 x x
Solve
2 4 x 2 (2) x 2 x 2 2 x x
2x2 + 2x = 4 x2 + x = 2 x2 + x 2 = 0 (x + 2)(x 1) = 0 x+2=0
x1=0
x = 2 or
x=1
Multiply each side by the LCD, x2.
Distributive Property Simplify. Divide each side by 2. Collect terms on one side. Factor the quadratic expression. Zero-Product Property Solve for x.
Check your solutions.
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
49
Name
Class
Date
Reteaching (continued)
11-5
Solving Rational Equations
Exercises Solve each equation. Check your solutions. 1.
1 2 3 x x
2.
4 6 10 2x 2x
3.
6 5 9 9b 3b
4.
1 5 8 20c 4c
6.
4 6 2 y y2
8.
2 4 2 z 1 z 1
5. 1
2 –1 x x2
7. 2 x 1
1 x2
9. Your sister can paint a room in 5 hours. Your dad can paint the same room in
1 hours. How long will it take your sister and your dad to paint the room if 2 they work together? 3
Solve each equation. Check your solutions. If there is no solution, write no solution.
10.
8 4 x 1 x 1
11.
6 2 x x 12 x 4
12.
5 1 2 – 12 4 x 3x
13.
4x 1 6 x x2 x–2
14.
5 1 5 x 7x 4 x
15.
6 4x 1 9( x 6) x6
2
Prentice Hall Algebra 1 • Teaching Resources Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
50
