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…

Question

asked Mar 26, 2017 168k views

2 Answers

Justin Moore · Answer 1 · 2017-04-01T23:00:09+0000

Answer:

Option (D) is correct.

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

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
a^2-b^2=(a+b)(a-b)

$\Rightarrow (8x-56)/(x^2-49)=(8x-56)/((x+7)(x-7))$

taking 8 common from numerator,

$\Rightarrow (8x-56)/((x+7)(x-7))=(8(x-7))/((x+7)(x-7))$

On simplifying , we get,

$\Rightarrow (8(x-7))/((x+7)(x-7))=(8)/((x+7))$

Consider second expression,

Solving quadratic using middle term splitting method,

$\Rightarrow (x-6)/(x^2+11x+28)=(x-6)/(x^2+7x+4x+28)$

$\Rightarrow (x-6)/(x^2+7x+4x+28)= (x-6)/((x+4)(x+7))$

Combining,

(8x-56)/(x^2-49)/ (x-6)/(x^2+11x+28)

$\Rightarrow (8)/((x+7))/ (x-6)/((x+4)(x+7))$

$\Rightarrow (8)/((x+7))* ((x+4)(x+7))/(x-6)$

On solving,

$\Rightarrow 8 * ((x+4))/(x-6)$

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

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