Question

Simplify for answer to question

Answer 1

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

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)

Answer 2

Answer: OPTION B.

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:

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

`(7x+42)/((x+6)(x+7))`

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

`(7(x+6))/((x+6)(x+7))`

- Finally, when you simplify, you obtain:

`(7)/(x+7)`