Question
Simplify the rational expression
2x^2+5x+3 / 6x+6
2x^2+5x+3 / 6x+6
Answers
Answered by
GPT 3.5
To simplify the rational expression (2x^2 + 5x + 3) / (6x + 6), you need to factor the numerator and the denominator and then cancel out any common factors.
Factor the numerator:
2x^2 + 5x + 3 can be factored into (2x + 3)(x + 1).
Factor the denominator:
6x + 6 = 6(x + 1).
Now, the rational expression becomes:
[(2x + 3)(x + 1)] / [6(x + 1)].
Notice that (x + 1) appears in both the numerator and the denominator. Cancel out these common factors:
[(2x + 3)(x + 1)] / [6(x + 1)] = (2x + 3) / 6.
So the simplified form of the rational expression is (2x + 3) / 6.
Factor the numerator:
2x^2 + 5x + 3 can be factored into (2x + 3)(x + 1).
Factor the denominator:
6x + 6 = 6(x + 1).
Now, the rational expression becomes:
[(2x + 3)(x + 1)] / [6(x + 1)].
Notice that (x + 1) appears in both the numerator and the denominator. Cancel out these common factors:
[(2x + 3)(x + 1)] / [6(x + 1)] = (2x + 3) / 6.
So the simplified form of the rational expression is (2x + 3) / 6.
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