Question

Simplify the expression

Answer 1

Option B:
`2x^2 +9x - 2/ 8x^3 +4x^2 -2x -1`

Explanation:

Given that:

`=(3/4x^2 + 4x +1) + (x+1/ 4x^2 - 1)`

By simplifying and factorizing we get:

`= (3/ 4x^2 + 2x + 2x +1) + (x+1/ (2x^2)-(1)^2)\\= (3/ 2x(2x+1)+1(2x + 1)) + (x+1/(2x+1)(2x - 1))\\= (3/(2x + 1)^2) + (x+1/ (2x+1)(2x -1))`

By taking LCM we get:

`=(3(2x-1)+ (x+1)(2x + 1))/((2x+ 1)^2 (2x-1))\\= 6x -3 + 2x^2 + x + 2x +1/ 8x^3 +4x^2 -2x -1\\= 2x^2 +9x -2/8x^3 +4x -2x -1`

I hope it will help you!