Simplify the following:

1.B

2.A

3. B

Step-by-step explanation:

1.

We have the denominator of the fraction as following:

As the initial one is a fraction, so that its denominator has to be different from 0.

=> () ≠ 0

⇔ (x +1) (x +5) ≠ 0

⇔ (x + 1) ≠ 0; (x +5) ≠ 0

⇔ x ≠ -1; x ≠ -5

Replace it into the initial equation, we have:

As (x+5) ≠ 0; we divide both numerator and denominator of the fraction by (x +5)

=>

So that with x ≠ 1; x ≠ -5

So that the answer is B.

2.

As the initial one is a fraction, so that its denominator has to be different from 0

=> x + 4 ≠ 0

=> x ≠ -4

As is also a fraction, so that its denominator (x-1) has to be different from 0

=> x - 1 ≠ 0

=> x ≠ 1

We have an equation:

=>

Replace it into the initial equation, we have:

As (x + 4) ≠ 0 (proven above), we can divide both numerator and the denominator of the fraction by (x +4)

=>

So that the initial equation is equal to with x ≠-4; x ≠1

=> So that the correct answer is A

3.

As the initial one is a fraction, so that its denominator (4x + x^2) has to be different from 0

We have:

(4x + x^2) = 4x + x.x = x ( x + 4)

So that:  (4x + x^2) ≠ 0 ⇔ x ( x + 4 ) ≠ 0

⇔  ⇔

As (4x + x^2) = x ( x + 4) , we replace this into the initial fraction and have:

As x ≠ 0, we can divide both numerator and denominator of the fraction by x and have:

So that with x ≠ 0; x ≠ -4

=> The correct answer is B