You need to add the given polynomials, hence, you need to remove the round brackets, such that:

`1/4x^9 + 1/3x^5 - 3/4x^2 + 11 - 1/2x^9 + 7/12x^5 - 3/8x^2`

You need to combine the like terms, hence you need to look for the terms that contain x raised to the same power, such that:

`(1/4 x^9 - 1/2 x^9) + (1/3x^5 + 7/12x^5) - (3/4 x^2 + 3/8 x^2) + 11`

You need to add the coefficients of like powers, such that:

`(1/2 - 1)*(1/2)*x^9 + (1 + 7/4)(1/3)x^5 - (1 + 1/2)(3/4)*x^2 + 11`

`-(1/4)x^9 + (11/12)x^5 - (9/8)x^2 + 11`

**Hence, performing the addition of polynomials, yields **`(1/4x^9 + 1/3x^5 - 3/4x^2 + 11) + (- 1/2x^9 + 7/12x^5 - 3/8x^2) = -(1/4)x^9 + (11/12)x^5 - (9/8)x^2 + 11.`

To simplify `(1/4x^9+1/3x^5-3/4x^2 +11)+(-1/2x^9 +7/12x^5-3/8x^2)`

you need to combine similar terms. Similar terms are those with the same variable with the same exponent. Before doing that, remove first the parentheses (). There is no problem on the first set. For the second set, to remove the (), you distribute + into the terms inside (), such that you treat + as +1 and multiply it with all the terms inside (). You'll have:

`1/4x^9 + 1/3x^5 -3/4x^2 +11 - 1/2x^9 + 7/12x^5 -3/8x^2`

`(1/4x^9 - 1/2x^9) + (1/3x^5+7/12x^5) + (-3/4x^2-3/8x^2) + 11`

`-1/4x^9 + 11/12x^5 -9/8x^2 +11====> answer`

`(1/(4x^9)+1/(3x^5)-3/(4x^2)+11)+(-1/(2x^9)+7/(12x^5)-3/(8x^2))`

`=1/(4x^9)-1/(2x^9)+1/(3x^5)+7/(12x^5)-3/(4x^2)-3/(8x^2)+11`

`=(1-2)/(4x^9)+(4+7)/(12x^5)-(6+3)/(8x^2)+11`

`=-1/(4x^9)+11/(12x^5)-9/(8x^2)+11`

Ans.