5-3 Adding & Subtracting Rational Expressions

5-3 Adding & Subtracting Rational Expressions

Part 1

Ex) Find the least common multiple of

 $2x^3y^{4\ }\ \&\ \ 3x^5y^3$ .

Write down the example before moving on for the first step.

The least common multiple of 2x³y⁴ and 3x⁵y³ is 6x⁵y^4.

• The smallest number 2 and 3 both go into is 6

• The largest number of x's is 5

• The largest number of y's is 4

• This results in a LCM of 6x⁵y⁴

Multiple Choice

Find the least common multiple of

 $6a^7b^3\ \ \&\ \ 8a^4b$ .

Use the last example for help. 

•  $48a^4b$  

•  $24a^{11}b^4$  

•  $48a^7b^4$  

•  $24a^7b^3$  

•  $24a^4b$  

Multiple Choice

Find the least common multiple of

 $9x^6y^4z\ \ \&\ \ x^3yz^2$  

•  $9x^6y^4z^2$  

•  $x^3yz$  

•  $18x^9y^5z^3$  

•  $x^9y^4z^2$  

•  $9x^3y^5z^3$  

Ex) Find the least common multiple of

 $x^2+3x-4\ \ \&\ \ x^2-3x+2$  

• You will factor each trinomial in order to find the least common multiple

Ex) Find the least common multiple of

 $x^2+3x-4\ \ \&\ \ x^2-3x+2$  

• Factored forms: $\left(x+4\right)\left(x-1\right)\ \ \&\ \ \left(x-2\right)\left(x-1\right)$  
  

• The least common multiple must include one of each different factor found in the trinomials.

• Although (x-1) comes up multiple times, it only exists once per factorization, so it only appears once in the least common multiple.

The least common multiple of

 $x^2+3x-4\ \ \&\ \ x^2-3x+2$  
is
 $\left(x+4\right)\left(x-1\right)\left(x-2\right)$  

Each different factor in the factorizations must be included.

Ex) Find the least common multiple of

 $2x^2-3x-2\ \ \&\ \ x^2-4$  

•  $2x^2-3x-2$   factored is (2x+1)(x-2)

•  $x^2-4$  is a difference of squares, which factors to (x-2)(x+2)

• There are three different factors: (2x+1), (x-2) and (x+2)

The least common multiple of

 $2x^2-3x-2\ \ \&\ \ x^2-4$  
is
(2x+1)(x-2)(x+2)

Multiple Choice

Select the least common multiple of
 $3x^2+7x-6\ \ \&\ \ 3x^2+8x-3$ . 

• (x+3)(3x-1)(3x-2)

• (3x-2)(x+3)(x+3)

• (x+3)(3x-1)(x+3)

• (x+3)(3x-1)

• (x+3)(3x-2)

Adding and subtracting rational expressions is similar to adding and subtracting fractions

• To add or subtract rational expressions with like denominators, add or subtract the numerators and use the same denominator.

• To add or subtract rational expressions with unlike denominators, find the least common denominator (LCD) of the polynomials in the denominators.

Multiple Choice

 $\frac{9x-1}{x^2+3}+\frac{x}{x^2+3}$  

•  $\frac{10x-1}{2x^2+6}$  

•  $\frac{10x-1}{x^2+3}$  

•  $\frac{8x-1}{x^4+9}$  

•  $\frac{8x-1}{x^2+3}$  

Multiple Choice

 $\frac{4x-2}{x+1}-\frac{3x^2+1}{x+1}$  

•  $\frac{3x^2-4x-3}{x+1}$  

•  $\frac{-3x^2-4x-1}{x+1}$  

•  $\frac{-3x^2+4x-3}{x+1}$  

•  $\frac{-3x^2+4x-1}{x+1}$  

Multiple Choice

 $\frac{2x+1}{x^2-2x-15}+\frac{4}{x-5}$  

•  $\frac{6x+1}{\left(x+3\right)\left(x-5\right)}$  

•  $\frac{2x+6}{x-5}$  

•  $\frac{2x+6}{\left(x+3\right)\left(x-5\right)}$  

•  $\frac{6x+13}{\left(x+3\right)\left(x-5\right)}$  

Multiple Choice

 $\frac{4}{x^2-9}-\frac{2}{x+3}$  

•  $\frac{-2x-2}{x^2-9}$  

•  $\frac{-2x+10}{x^2-9}$  

•  $\frac{2}{x-3}$  

•  $\frac{2x-2}{x-3}$