Question

Simplify the given expression.

Answer 1

(8x - 21) / (2x + 7)(2x - 7)

Explanation:

7 / (4x^2 - 49)+ 4 / (2x + 7)

= 7 / (2x + 7)(2x - 7) + 4 / (2x + 7)

LCM = (2x + 7)(2x - 7) so we have

(7 + 4(2x - 7) / (2x + 7)(2x - 7)

= (8x - 21) / (2x + 7)(2x - 7).

Answer 2

8x-21

----------------------

(2x-7)(2x+7)

Explanation:

7 4

----------- + ------------

4x^2 -49 2x+7

Factor ( notice that it is the difference of squares)

7 4

----------- + ------------

(2x)^2 - 7^2 2x+7

7 4

----------- + ------------

(2x-7)(2x+7) 2x+7

Get a common denominator

7 4(2x-7)

----------- + ------------

(2x-7)(2x+7) (2x-7)(2x+7)

Combine

7 +4(2x-7)

----------------------

(2x-7)(2x+7)

7 +8x-28

----------------------

(2x-7)(2x+7)

8x-21

----------------------

(2x-7)(2x+7)