What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared minus 14x minus 15

6 times the quantity 2 x plus 5 end quantity over the quantity 2x minus 5 end quantity times 4 x plus 3

6 over the quantity 4 x plus 3

6 times the quantity x plus 1 end quantity over the quantity 2x minus 5 end quantity times 4 x plus 3

6 times the quantity x plus 1 end quantity over the quantity 2x plus 5 end quantity times 4 x plus 3

First we have to factorize:

8 x² - 14 x - 15 = 8 x² - 20 x + 6 x - 15 =

= 4 x (2 x - 5) + 3 (2 x - 5) =

= (2 x - 5) (4 x + 3)

Then we will put it into the equation:

3 / (4 x + 3) + 21 / (2 x - 5) (4 x + 3) =

= 3 (2 x - 5) + 21 / (2 x - 5) (4 x + 3) =

= 6 x - 15 + 21 / (2 x - 5) (4 x + 3) =

= (6 x + 6) / (2 x - 5) (4 x + 3) =

= 6 (x + 1) / (2 x - 5) (4 x + 3)

Answer: C) 6 times the quantity x plus 1 end over the quantity 2 x minus 5 end quantity times 4 x plus 3.