Question

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

Answer 1

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)