What is the simplified form of 3 over 4x + 3 plus 21 over 8x² - 14x - 15?

Solution:

Given (3/4x+3) + (21/8x² -14x -15)

⇒ (3/4x+3) + (21/ 8x² +6x -20x -15) (Factorizing polynomials by splitting the middle terms)

⇒ (3/4x+3) + (21/ 2x(4x +3) -5(4x+3))

⇒ 3/(4x+3) + (21/ (4x +3)(2x -5))

⇒ 3/(4x+3) [1 +7/(2x-5)](Taking out 3/(4x+3) as a common factor)

⇒ 3/(4x+3) [(2x-5+7)/(2x-5)]

⇒ 3/(4x+3) [(2x+2)/(2x-5)]

⇒ 3/(4x+3) [2(x+1)/(2x-5)]

⇒ 6(x+1)/(4x+3)(2x-5)

What is the simplified form of 3 over 4x + 3 plus 21 over 8x² - 14x - 15?

Summary:

The simplified form of 3 over 4x + 3 plus 21 over 8x² - 14x - 15 is 6(x+1)/(4x+3)(2x-5).