What is the simplified form of 3 over 2x minus 5 + 21 over 8 x squared minus 14x minus 15?

Solution:

The above statement can be put mathematically as follows:

3/(2x - 5) + 21/ (8x² - 14x - 15) --- (1)

The denominator of the term on the right hand side of the + sign can be factorized as follows:

8x² - 20x + 6x - 15

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

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

Therefore equation (1) can be rewritten as

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

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

= (12x + 9 + 21)/[(2x - 5)(4x + 3)])

= (12x + 30)/[(2x - 5)(4x + 3)])

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

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

Summary:

The simplified for of the given algebraic expression 3 over 2x minus 5 + 21 over 8 x squared minus 14x minus 15 is 6(2x + 5)/(2x - 5)(4x + 3)