(f+g)(x)=(x+9)+(4x^2)

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Solution for (f+g)(x)=(x+9)+(4x^2) equation: 


Simplifying
(f + g)(x) = (x + 9) + (4x2)

Reorder the terms for easier multiplication:
x(f + g) = (x + 9) + (4x2)
(f * x + g * x) = (x + 9) + (4x2)
(fx + gx) = (x + 9) + (4x2)

Reorder the terms:
fx + gx = (9 + x) + (4x2)

Remove parenthesis around (9 + x)
fx + gx = 9 + x + (4x2)

Solving
fx + gx = 9 + x + (4x2)

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Add '-1gx' to each side of the equation.
fx + gx + -1gx = 9 + x + -1gx + (4x2)

Combine like terms: gx + -1gx = 0
fx + 0 = 9 + x + -1gx + (4x2)
fx = 9 + x + -1gx + (4x2)

Reorder the terms:
fx = 9 + -1gx + x + (4x2)

Divide each side by 'x'.
f = 9x-1 + -1g + 1 + (4x)

Simplifying
f = 9x-1 + -1g + 1 + (4x)

Reorder the terms:
f = 1 + -1g + 9x-1 + (4x)

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