Simplify. x^2-3x-18/x+3 x - 3 x - 6 where x -3 x - 6 where x 6 1/x+3 where x -3 simplify x-2/x^2+4x-12 1/x+6 where x -6 1/x+6 where x -6,2 1/x+2 where x -2 x+2 simplify 5x^3/7 x^3+x^4 5/7+x where c 0,-7 5/7+x where x -7 5/7x where x 0 5/7 simplify x/6x-x^2 1/6-x where x 0,6 1/6-x where x 6 1/6x where x 0 1/6

1. Option C is correct

2. Option A is correct

3. Option C is correct

4. Option B is correct

5. Option D is correct

Step-by-step explanation:

1. x^2-3x-18/x+3

Factorize the numerator

x^2-6x+3x-18/x+3

x(x-6)+3(x-6)/x+3

(x+3)(x-6)/x+3

x-6

x-6 where x≠6

Option C is correct.

2. x-2/x^2+4x-12

Factorizing the denominator

x-2/x^2+6x-2x-12

x-2/x(x+6)-2(x+6)

x-2/(x-2)(x+6)

1/x+6

1/x+6 where x≠-6

Option A is correct.

3. 5x^3/7 x^3+x^4

5x^3/7x^3+x^4

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

5/7+x

Option C is correct

5/7+x where x≠-7

4. Simplify x/6x-x^2

x/6x-x^2

x/x(6-x)

1/6-x

Option B is correct

1/6-x where x≠6

5. 2/3a * 2/a^2

Multiplying both terms

4/3a^3

Option D is correct.

4/3a^3 where a≠0

the infinity sign

step-by-step explanation: