ADDING AND SUBTRACTING RATIONAL EXPRESSIONS:

MULTIPLICATION:

COMBINE RIGHT ACROSS THE MULTIPLICATION SIGN.

DIVISION:

FLIP THE SECOND RATIONAL AND MULTIPLY

ADDING & SUBTRACTING LIKE DENOMINATORS

1. Add or subtract the numerators by combining like terms and put over the denominator

2. Follow the steps for simplifyingExample 1:

𝑥𝑥2−4

−2

𝑥2−4

𝑥−2𝑥2−4

𝑥−2(𝑥−2)(𝑥+2)

1𝑥+2

Example 2:

95−𝑥

+45−𝑥

9+45−𝑥

135−𝑥

𝑥2

𝑥3+27−

3𝑥𝑥3+27

+ 9𝑥3+27

Example 3:

𝑥2−3 𝑥+9𝑥3+27

𝑥2−3 𝑥+9(𝑥+3)(𝑥2−3𝑥+9)

ADDING & SUBTRACTING UNLIKE DENOMINATORS

1. Factor the denominators and determine the LCD

2. Rewrite each fraction over the LCD

3. Add or subtract the numerators by combining like terms and put over the denominator

4. Follow the steps for simplifying

http://www.khanacademy.org/math/algebra/rational-expressions/rational_expressions/v/adding-and-subtracting-rational-expressions

❑5𝑥𝑦

❑3𝑥∙

33 ∙

5 𝑦5 𝑦

❑15𝑥𝑦

− ❑15𝑥𝑦

Example 4:

❑5𝑥𝑦

− ❑3𝑥

Example 5: ❑64 𝑥3−27

+ ❑2𝑥

❑(4 𝑥−3)(16 𝑥2+12 𝑥+9)❑2𝑥

∙2 𝑥2 𝑥

∙(4 𝑥−3)(16 𝑥2+12𝑥+9)(4 𝑥−3)(16 𝑥2+12𝑥+9)

❑2𝑥 (4 𝑥−3)(16 𝑥2+12 𝑥+9)

+ ❑2𝑥 (4 𝑥−3)(16 𝑥2+12 𝑥+9)

Example 6:

159𝑥

+518 𝑥

159𝑥

518𝑥

∙22=3018 𝑥

3018𝑥

+518 𝑥

=3518 𝑥

5

6 𝑥2∙2 (𝑥−3)2 (𝑥−3)𝑥

4 𝑥 (𝑥−3)∙3 𝑥3 𝑥

Example 7:

5

6 𝑥2+

𝑥4 𝑥2−12𝑥

¿10 (𝑥−3)12𝑥2(𝑥−3)

¿ 3 𝑥2

12𝑥2(𝑥−3)

10(𝑥−3)12𝑥2(𝑥−3)

+ 3 𝑥2

12𝑥2(𝑥−3)

10 (𝑥−3 )+3𝑥2

12𝑥2(𝑥−3)

1𝑥+5

−2

2𝑥−10+2 𝑥

𝑥2−25

Example 3:

1𝑥+5

−2

2(𝑥−5)+

2𝑥(𝑥−5)(𝑥+5)

2(𝑥−5)2(𝑥+5)(𝑥−5)

−2(𝑥+5)

2(𝑥+5)(𝑥−5)+2 𝑥 ∙2

2(𝑥+5)(𝑥−5)