Adding/Subtracting Rational Expressions

Adding/Subtracting Rational Expressions

Adding and Subtracting Rational Expressions

• When we add or subtract rational expressions we need to find a common denominator (if there is not already one given)

Once we have a common denominator...

• When adding, combine like terms in the numerator and keep the denominator as is

• When subtracting, distribute the negative sign into the numerator of the second fraction and keep the denominator as is

Open Ended

What is the common denominator between these two fractions:  $\frac{x}{3}$ and  $\frac{x}{x-5}$  

Multiple Choice

What is the common denominator between these three fractions:  $\frac{x}{2},\ \frac{3}{x},\ and\ \frac{6}{x^4}$  

•  $2x^5$  

•  $2x^4$  

•  $2x$  

•  $x^5$  

Open Ended

Add:  $\frac{3+x}{4}+\frac{7x-9}{4}$  

Multiple Choice

Subtract:  $\frac{6x^2+4x-1}{x-4}-\frac{2x^3+3x^2-2x+5}{x-4}$  

•  $\frac{4x^2-3x^2+6x-6}{\left(x-4\right)^2}$  

•  $\frac{-2x^3+9x^2+2x+4}{x-4}$  

•  $\frac{-2x^3+3x^2+6x-6}{x-4}$  

•  $\frac{x^2+6x-6}{\left(x-4\right)^2}$  

Finding equivalent fractions:

• When you don't have a common denominator, you have to find one like we did in the first two examples

• Then we need to write equivalent fractions for each fraction given

• Then we can add or subtract

• **Remember** we still need to find the values that make the denominator 0. These values are still where our expression is undefined.

Example: Add

 $\frac{3}{x}+\frac{7-x}{4}$ 

Common denominator: 4x
Multiply the first fraction by  $\frac{4}{4}$  and the second fraction by  $\frac{x}{x}$   
Write the equivalent expression:  $\frac{12}{4x}+\frac{x\left(7-x\right)}{4x}$  
We can now write this as one fraction:  $\frac{12+x\left(7-x\right)}{4x}$  
Distribute and combine like terms:  $\frac{-x^2+7x+12}{4x}$   $x\ne0$  

Example: Subtract

 $\frac{3x}{2xy}-\frac{2y}{3y^3}$  

Common denominator:  $6xy^3$   
Multiply the first fraction by  $\frac{3y^2}{3y^2}$  and the second fraction by  $\frac{2x}{2x}$  

Write the equivalent fractions:  $\frac{9xy^2}{6xy^3}-\frac{4xy}{6xy^3}$  
Write as one fraction:  $\frac{9xy^2-4xy}{6xy^3}$  
There are no like terms here, so you cannot combine anything. HOWEVER, you can simplify!  $\frac{9y-4}{6y^2},\ y\ne0$  (divide ALL terms by xy)

Examples on Jamboard

We are going to do a few examples together on a Jamboard and then we'll come back and answer some questions on here.

Multiple Choice

Perform the indicated operation: 

Multiple Choice

Is y defined at 0?

• Yes

• No

Multiple Choice

Perform the indicated operation:

Multiple Choice

Is x defined at 1?

• Yes

• No

Multiple Choice

Perform the indicated operation:

Open Ended

State the restrictions:

Multiple Choice

Perform the indicated operation:

Open Ended

State the restrictions:

Multiple Choice

Perform the indicated operation:

Multiple Choice

Is n defined at -4?

• Yes

• No

Multiple Choice

Perform the indicated operation:

Multiple Select

Check all the values that x cannot be:

• 0

• 1

• 5

• 1/5

Multiple Choice

Perform the indicated operation:

Open Ended

State the restrictions:

Multiple Choice

Perform the indicated operation:

Multiple Choice

Is x defined at 0?

• Yes

• No

Open Ended

Perform the indicated operation and state the restrictions:

Open Ended

Perform the indicated operation and state the restrictions:

Poll

How confident are you in adding and subtracting rational expressions?

• I got this!

• I'm somewhere in the middle

• I need more practice