Simplfying rational expressions

AI Thread Summary
The discussion focuses on simplifying the rational expression (6x² + 17x + 7) / (2x² + 7x + 3). Participants explore factoring the numerator and denominator into binomial factors. The correct factorization for the numerator is (2x + 1)(3x + 7) and for the denominator, it is (2x + 1)(x + 3). After simplification, the final expression is determined to be (3x + 7) / (x + 3). The conversation emphasizes the importance of factoring trinomials to solve the problem effectively.
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Homework Statement



6x (squared) +17x+7
_________________
2x sqaured + 7x +3

Homework Equations



Simplify

The Attempt at a Solution



3x+7 is the answer
____
x+3
maybe u can factor 6x by doing 2x (3x) or maybe u don't do that and take 6x (squared +17
_____________
2x squared +7
im not sure
 
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Do you know how to factor trinomials into two binomial factors? That's the key to this problem.

6x2 + 17x + 7 = (2x + ?)(3x + ?)

2x2 + 7x + 3 = (2x + ?)(x + ?)

Fill in the question marks.
 
6x2 + 17x + 7 = (2x + ?)(3x + ?)

2x2 + 7x + 3 = (2x + ?)(x + ?)
(2x + 1) (3x+7)

(2x +1)(x + 3)

ok nice thanks alot
 

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