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Simplify completely the expression (x² + 12x + 35) / (3x + 15).

1) (x² + 21) / 3
2) (x² + 11) / 3
3) (x + 7) / 3
4) (x + 5) / 3

User Kvista
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1 Answer

5 votes

Final answer:

The expression
(x² + 12x + 35) / (3x + 15) simplifies to
(x + 7) / 3 after factoring and canceling out common terms; therefore, the correct answer is option
3.

Step-by-step explanation:

To simplify completely the expression
(x² + 12x + 35) / (3x + 15),

we should factor both the numerator and the denominator, if possible.

The numerator factors to
(x + 5)(x + 7) because
x² + 12x + 35 is a quadratic expression that can be factored into two binomials whose product gives the original quadratic.

On the other hand, the denominator,
3x + 15, can be simplified by factoring out the common factor of 3,

which gives us
3(x + 5).

After factoring we have the following expression:


((x + 5)(x + 7)) / (3(x + 5)).

We notice that
(x + 5) appears in both the numerator and the denominator, so we can cancel this term out.

After canceling, the expression simplifies to
(x + 7) / 3.

Therefore, the correctly simplified expression is option
3: (x + 7) / 3.

User Bemug
by
8.4k points

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