Simplification of rational expressions I have the following expression: <mrow class="MJX-TeXA

Augustus Acevedo 2022-07-07 Answered
Simplification of rational expressions
I have the following expression:
2 x 2 + 2 x 2 5 x + 6
So I can simplify this as:
2 x 2 + 2 ( x 3 ) ( x 2 )
I make the common denominator to be ( x 3 ) ( x 2 )
So I then apply ( x 3 ) to the left hand side which gives me:
2 ( x 3 ) + 2 ( x 3 ) ( x 2 )
I have clearly taken a wrong step because the answer in the book to the original expression is 2 x 3 so I'm not sure how that answer was arrived at.
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Answers (2)

zlepljalz2
Answered 2022-07-08 Author has 22 answers
You did nothing wrong. Note that the numerator can be written as
2 ( x 3 ) + 2 = 2 x 6 + 2 = 2 x 4 = 2 ( x 2 ) .

We have step-by-step solutions for your answer!

aangenaamyj
Answered 2022-07-09 Author has 5 answers
Notice, the following steps
2 x 2 + 2 x 2 5 x + 6
= 2 ( 1 x 2 + 1 ( x 2 ) ( x 3 ) )
= 2 x 2 ( 1 + 1 x 3 )
= 2 x 2 ( x 3 + 1 x 3 )
= 2 x 2 ( x 2 x 3 )
= 2 x 3
Your book has the correct expression.

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