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)
