Answer:
(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).
8x-21
----------------------
(2x-7)(2x+7)
7 4
----------- + ------------
4x^2 -49 2x+7
Factor ( notice that it is the difference of squares)
(2x)^2 - 7^2 2x+7
(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)
7 +8x-28
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