Question

Simplify for answer to question

Answer 1

Answer: OPTION B.

Step-by-step explanation:

You must:

- Factor the denominnator of the expression. Find two number whose sum is 12 and whose product is 42, these would be 6 and 7, then:

$\frac{7x+42}{x^{2}+13x+42}$

$\frac{7x+42}{(x+6)(x+7)}$

- Now, you must factor out 7 in the numerator, as following:

$\frac{7(x+6)}{(x+6)(x+7)}$

- Finally, when you simplify, you obtain:

$\frac{7}{x+7}$

Answer 2

Answer:

The correct answer is Option B. 7/(x+7)

Step-by-step explanation:

The given expression is ,

(7x + 42)/(x^2 + 13x + 42)

To simplify the expression

(7x + 42)/(x^2 + 13x + 42)

Simplify (7x + 42)

7x + 42 = 7(x + 6)   (Taking 7 as common)

Simplify (x^2 + 13x + 42)

(x^2 + 13x + 42) = x^2 + 7x + 6x + 42

  = x(x + 7) + 6(x + 7)

  = (x + 7)(x+6)

Then we can write,

(7x + 42)/(x^2 + 13x + 42) = 7(x + 6)/(x + 7)(x+6) = 7/(x+7)

Therefore the correct answer is option B. 7/(x+7)