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- Algeraic 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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22.
Algeraic Fractions
22.1
Simplifying algebraic fractions and restrictions
22.2
Adding and subtracting algebraic fractions
22.3
Multiplying algebraic fractions
22.4
Dividing algebraic fractions
22.5
Solving equations with algebraic fractions
22.6
Applications of equations with algebraic fractions
22.7
Simplifying complex fractions
22.8
Partial fraction decomposition