Today's soundtrack is Ancient Celtic Roots, a compilation CD that my wife gave me for my birthday several years ago. Unfortunately, I couldn't find it anywhere on Spotify, so I wasn't able to add it to the Blogging Playlist.
To add or subtract rational expressions with monomial denominators (say that five times fast!), we must first find the least common multiple (LCM) of the expressions. Only then can we find the sum or difference.
We'll be learning three skills today:
Adding rational expressions with monomial denominators
Subtracting rational expressions with monomial denominators
Simplify three or more "rational expressions involving more than one operation" (Pearson's Pre-Calculus 11, p. 552)
Let's get to it!
How to add two rational expressions with monomial denominators
Find the non-permissible values of each denominator
Using a factor tree, find the factors of each denominator (including variables)
Find the least common multiple (LCM), which is the "product of the greatest power of each factor in any list" (Pearson's Pre-Calculus 11, p. 550).
Divide the LCM found in step 3 by the denominator of the first expression
Multiply both the numerator and the denominator of the first expression by the quotient found in step 4, using the distributive property if necessary
This gives us an equivalent form of the first expression
Divide the LCM found in step 3 by the denominator of the second expression
Multiply both the numerator and the denominator of the second expression by the quotient found in step 6, using the distributive property if necessary
This gives us an equivalent form of the second expression
Add the expressions found in steps 5 and 7 together, combining like terms
This gives us the sum of the two expression
List any non-permissible values in addition to those found in step 1
How to subtract two rational expressions with monomial denominators
Find the non-permissible values of each denominator
Using a factor tree, find the factors of each denominator (including variables)
Find the least common multiple (LCM), which is the "product of the greatest power of each factor in any list" (p. 550).
Divide the LCM found in step 3 by the denominator of the first expression
Multiply both the numerator and the denominator of the first expression by the quotient found in step 4, using the distributive property if necessary
This gives us an equivalent form of the first expression
Divide the LCM found in step 3 by the denominator of the second expression
Multiply both the numerator and the denominator of the second expression by the quotient found in step 6, using the distributive property if necessary
This gives us an equivalent form of the second expression
Subtract the second the expression found in step 7 from the first expression found in step 5
This gives us the sum of the two expression
Combine like terms
List any non-permissible values in addition to those found in step 1
How to simplify three or more rational expressions with monomial denominators when we must perform more than one operation
If we have three or more expressions to solve and we need to perform more than one operation (for example, [3/2a] + [w+3/5aw] - [8w/3a]), we must do the following:
Find the non-permissible values of each denominator
Using a factor tree, find the factors of each denominator (including variables)
Find the least common multiple (LCM)
Divide the LCM found in step 3 by the denominator of each expression
Multiply both the numerator and the denominator of each expression by the respective quotients found in step 4, using the distributive property if necessary
This gives us an equivalent form of each
Over the single denominator, put each of the numerators in brackets, putting the correct positive or negative symbol above it
Combine like terms
List any non-permissible values in addition to those found in step 1
And Bob's your uncle! That's all for today.