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

3 / (4x+3) + 21 / (8x^2-14-15)

The LCD is) (4x+3) * 8x^2-14x-15).

Multiply each fraction by the LCD.

[3 (8x^2-14x-15) + 21 (4x+3) ]/LCD

Simplify the numerator.

(24x^2+42x+18) / LCD

Factor numerator.

[6 (4x+3) (x+1) ] / (4x+3) (8x^2-14x-15)

Factor (8x^2-14x-15).

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

[6 (4x+3) (x+1) ] / (4x+3) ^2 (2x-5)

Cancel out common terms in the numerator and denominator.

Answer:

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