Addition and Subtraction of Rational Expressions

1.  \rhd Adding and Subtracting rational expressions with like denominators (3:45)  This video contains one example of adding and one of subtracting rational expressions, namely:

[Example 1]  \dfrac{6}{2x^2-7} + \dfrac{-3x-8}{2x^2-7} = \dfrac{-2-3x}{2x^2-7}

[Example 2]  \dfrac{9x^2 +3}{14x^2 - 9} - \dfrac{-3x^2+5}{14x^2 - 9} = \dfrac{12x^2 - 2}{14x^2 - 9}

2.  \star Practice: Adding and subtracting rational expressions with like denominators. Problems similar to:  \dfrac{19m+3m^3}{14m-3} - \dfrac{12m^2 + 3m}{14m-3}. (4 problems)

3. \rhd Adding rational expressions with unlike denominators (2:43)  \dfrac{a}{b} + \dfrac{c}{d}.

4. \star Practice: Adding rational expressions with unlike denominators. Problems similar to \dfrac{8}{x+2}-\dfrac{6}{x+5}. (4 problems)

5. \rhd Adding rational expressions: unlike denominators (5:11)  Problems such as \dfrac{5x}{2x-3} + \dfrac{-4x^2}{3x+1} = \dfrac{-8x^3 + 27x^2 +5x}{(2x-3)(3x+1)}.

6. \rhd Subtracting rational expressions: unlike denominators (4:47)  Solving \dfrac{-5x}{8x+7} - \dfrac{6x^3}{3x+1} = \dfrac{-48x^4 - 42x^3 - 15x^2 - 5x}{(8x+7)(3x+1)}.

7. \star Practice: Adding rational expressions with unlike denominators. Problems such as \dfrac{9}{x-7} + \dfrac{3}{x}. (4 problems)

8. \rhd Finding the least common multiple of two integers (4:15)

[Example 1] Find the \mathrm{lcm} of 36 and 12.

[Example 2] Find the \mathrm{lcm} of 12 and 18 (uses the prime factorization method).

9.  \rhd Finding the least common multiple with repeating factors (2:34)  Find the \mathrm{lcm}(30,25).

10. \star Practice: Find the least common multiple of two integers.   Find the \mathrm{lcm}(6,10). (4 problems)

11. \rhd Finding the least common multiple of polynomials (6:51)
Finds the least common multiple of 3z^3-6z^2-9z and 7z^4 + 21z^3 +14z^2.

12. \rhd Subtracting rational expressions (4:48) \dfrac{-z^3}{(z+8)(9z-5)} - \dfrac{3}{(z+6)(9z-5)}.

13. \star  Practice: Combine the rational expressions.  Problems such as \dfrac{9}{x^2-12x+36} + \dfrac{x}{x^2-36}. (4 problems)