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- Algebraic Fractions
Adding and subtracting rational expressions
- Intro Lesson13:29
- Lesson: 1a0:31
- Lesson: 1b1:14
- Lesson: 2a2:58
- Lesson: 2b1:48
- Lesson: 2c2:38
- Lesson: 3a3:23
- Lesson: 3b5:16
- Lesson: 4a1:07
- Lesson: 4b1:25
- Lesson: 4c1:52
- Lesson: 4d3:25
- Lesson: 5a2:42
- Lesson: 5b2:20
- Lesson: 5c3:34
- Lesson: 5d4:26
- Lesson: 6a3:55
- Lesson: 6b3:33
- Lesson: 6c6:15
- Lesson: 76:24
- Lesson: 8a2:55
- Lesson: 8b4:27
- Lesson: 8c8:12
- Lesson: 95:24
- Lesson: 105:13
- Lesson: 11a4:07
- Lesson: 11b12:52
- Lesson: 11c6:12
- Lesson: 129:50
Adding and subtracting rational expressions
When adding and subtracting rational expressions, the denominators of the expressions will dictate how we solve the questions. Different denominators in the expressions, for example, common denominators, different monomial/binomial denominators, and denominators with factors in common, will require different treatments. In addition, we need to keep in mind the restrictions on variables.
Basic Concepts: Common factors of polynomials, Factoring polynomials: ax2+bx+c, Factoring perfect square trinomials: (a+b)2=a2+2ab+b2 or (a−b)2=a2−2ab+b2, Find the difference of squares: (a−b)(a+b)=(a2−b2), Solving polynomial equations
Related Concepts: Solving rational equations, Integration of rational functions by partial fractions
Lessons
- Introductionreview – adding/subtracting fractions
- 1.Simplify:a)133+138b)23+54
- 2.Simplify:a)6x+32x−45xb)3y−3+62y+3c)33a−5−22a−1
- 3.Simplify:a)95x−3+6x−33x−2b)3−4y−1−64−3y
- 4.Adding and Subtracting with Common Denominators State any restrictions on the variables, then simplify:a)x3+x12−x5b)3a6a−2+3a−10a+2c)6m−56m−6m−55d)2x−39x−1−2x−38+3x
- 5.Adding and Subtracting with Different Monomial Denominators State any restrictions on the variables, then simplify:a)4m3+5m2b)4x5−67c)10x2x−3−5x3x−2d)3yy−1−2y22
- 6.Adding and Subtracting with Different Monomial/Binomial Denominators State any restrictions on the variables, then simplify:a)3xx−4+x−25xb)3m+25−4m−71c)2x+36x−1−4x+51−x
- 7.State any restrictions on the variables, then simplify: x+21−x−15+x3
- 8.Denominators with Factors in Common State any restrictions on the variables, then simplify:a)4x5−12x5b)3x+94+2x+65c)x2−5x3−x28
- 9.Denominators with Factors in Common State any restrictions on the variables, then simplify: (x−1)(x+3)5+(x+2)(x−1)4
- 10.State any restrictions on the variables, then simplify: x2−9x+x−35
- 11.State any restrictions on the variables, then simplify:a)x−34−x2−2x−35−xb)a2−a−23+a2+3a+25c)x2+4x+41−x2+5x+64
- 12.State any restrictions on the variables, then simplify: x2−2x−3x2−5x+6−x2+7x+10x2+9x+20
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12.
Algebraic Fractions
12.1
Simplifying algebraic fractions and restrictions
12.2
Adding and subtracting algebraic fractions
12.3
Multiplying algebraic fractions
12.4
Dividing algebraic fractions
12.5
Solving equations with algebraic fractions
12.6
Applications of equations with algebraic fractions
12.7
Simplifying complex fractions
12.8
Partial fraction decomposition