Simplify completely quantity 8 x minus 56 over quantity x squared minus 49 divided by quantity x minus 6 over quantity x squared plus 11 x plus 28

a. 4 open parentheses x plus 4 close parentheses over quantity x minus 3

b. 8 open parentheses x plus 2 close parentheses over quantity x minus 3

c. 8 open parentheses x plus 4 close parentheses over quantity x minus 7

d. 8 open parentheses x plus 4 close parentheses over quantity x minus 6

Option (D) is correct.

8 open parentheses x plus 4 close parentheses over quantity x minus 6

Step-by-step explanation:

Given : 8 x minus 56 over quantity x squared minus 49 divided by quantity x minus 6 over quantity x squared plus 11 x plus 28

We need to simplify above and choose one correct option out of given options.

First writing each term mathematically,

8 x minus 56 over quantity x squared minus 49 is written as ,

quantity x minus 6 over quantity x squared plus 11 x plus 28 is written as,

Combining, we get,  8 x minus 56 over quantity x squared minus 49 divided by quantity x minus 6 over quantity x squared plus 11 x plus 28 as

Solving fraction separately, we get,

Consider first expression,

Applying identity

taking 8 common from numerator,

On simplifying , we get,

Consider second expression,  

Solving quadratic using middle term splitting method,

Combining,

On solving,

Thus, we obtain (D) is as correct option.

8 open parentheses x plus 4 close parentheses over quantity x minus 6

the answer is a

step-by-step explanation: