How do I solve this, first I have to factor 2 x </mrow> x

Kapalci 2022-06-24 Answered
How do I solve this, first I have to factor 2 x x 1 + 3 x + 1 x 1 1 + 9 x + 2 x 2 x 2 1
the solution is
3 x x + 1
The only advance that I have done is factor x 2 1= ( x 1 ) ( x + 1 )
do not know how can I factor 1 + 9 x + 2 x 2 can someone please guide me in how to solve this exercise.
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Answers (2)

Ethen Valentine
Answered 2022-06-25 Author has 15 answers
The first two terms are already over a common denominator.
First simplify
2 x x 1 + 3 x + 1 x 1 1 + 9 x + 2 x 2 x 2 1 = 5 x + 1 x 1 1 + 9 x + 2 x 2 x 2 1
Then put the first fraction over the same denominator as the second
( 5 x + 1 ) ( x + 1 ) x 2 1 1 + 9 x + 2 x 2 x 2 1 = ( 5 x + 1 ) ( x + 1 ) ( 1 + 9 x + 2 x 2 ) x 2 1
Now simplify the numerator

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Petrovcic2x
Answered 2022-06-26 Author has 11 answers
Notice that
A B + A B C = C C A B + A B C = A C + A B C
Then
( x + 1 ) ( x + 1 ) 2 x ( x 1 ) + ( x + 1 ) ( x + 1 ) 3 x + 1 ( x 1 ) + 1 + 9 x + 2 x 2 ( x 1 ) ( x + 1 ) = 2 x ( x + 1 ) + ( 3 x + 1 ) ( x + 1 ) ( 1 + 9 x + 2 x 2 ) ( x 1 ) ( x + 1 ) = 2 x 2 + 2 x + 3 x 2 + 3 x + x + 1 1 9 x 2 x 2 ( x 1 ) ( x + 1 ) = 3 x 2 3 x ( x 1 ) ( x + 1 )

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