Addition and Subtraction of Rational Expressions

1.  $⊳$ 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]  ${\displaystyle \frac{6}{2x^2-7}}+{\displaystyle \frac{-3x-8}{2x^2-7}}={\displaystyle \frac{-2-3x}{2x^2-7}}$

[Example 2]  ${\displaystyle \frac{9x^2+3}{14x^2–9}}–{\displaystyle \frac{-3x^2+5}{14x^2–9}}={\displaystyle \frac{12x^2–2}{14x^2–9}}$

2.  $\star$ Practice: Adding and subtracting rational expressions with like denominators. Problems similar to:  . (4 problems)

3. $⊳$ Adding rational expressions with unlike denominators (2:43)  ${\displaystyle \frac{a}{b}}+{\displaystyle \frac{c}{d}}$.

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

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

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

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

8. $⊳$ 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.  $⊳$ 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. $⊳$ 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. $⊳$ Subtracting rational expressions (4:48) .

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