GIVING OUT BRAINLIEST TO WHOEVER GETS ALL OF THEM RIGHT 4.Simplify x/7x+x^2
A. 1/7+x; where x≠-7
B.1/7x;where x≠0
C.1/7+x; where x≠0,-7
D.1/7;

5.Simplify -14x^3/x^3-5x^4
A. -14/5x-1; where x≠1/5,0
B.-14x/1-5x;where x≠1/5
C.1-5x/-14x; where x≠0
D.-14/1-5x; where x≠1/5,0

6.Simplify x+7/x^2+4x-21
A. 1/x-3; where x≠3,-7
B. x-3;where x≠3
C.1/x-7; where x≠7
D. x-7

7.Simplify x^2+3x-4/x+4
A. 1/x-4; where x≠4
B. x-4;
C. x-1; where x≠1
D. x-1; where x≠-4

8.Simplify 2/3a*2/a^2
A. 4/3a^2; where a≠0
B.1/a^2;where a≠0
C.4/3a^3; where a≠0
D.4/3a^2

4) is equivalent to for all . ( A)

5) is equivalent to for all . ( B)

6) is equivalent to for all . ( None)

7) is equivalent to . ( None)

8)   is equivalent to for all . ( A)

Step-by-step explanation:

We proceed to simplify each expression below:

4)

(i) Given

(ii) Distributive property

(iii) Distributive property

(iv) Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

Hence, we conclude that is equivalent to for all . ( A)

5)

(i) Given

(ii) Distributive property

(iii) Distributive property

(iv) Commutative property/Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

Hence, we conclude that is equivalent to for all . ( B)

6)

(i) Given

(ii)

(iii) Commutative and distributive properties.

(iv) Existence of multiplicative inverse/Modulative property/Result

Rational functions are undefined when denominator equals 0. That is:

Hence, we conclude that is equivalent to for all . ( None)

7)

(i) Given

(ii)  

(iii) Commutative and distributive properties.

(iv) Existence of additive inverse/Modulative property/Result

Polynomic function are defined for all value of .

is equivalent to . ( None)

8)

(i)

(ii) /Result

Rational functions are undefined when denominator equals 0. That is:

Hence, is equivalent to for all . ( A)