(f-g)(x)=(2t^2-1)-(2t-2)

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Solution for (f-g)(x)=(2t^2-1)-(2t-2) equation: 


Simplifying
(f + -1g)(x) = (2t2 + -1) + -1(2t + -2)

Reorder the terms for easier multiplication:
x(f + -1g) = (2t2 + -1) + -1(2t + -2)
(f * x + -1g * x) = (2t2 + -1) + -1(2t + -2)
(fx + -1gx) = (2t2 + -1) + -1(2t + -2)

Reorder the terms:
fx + -1gx = (-1 + 2t2) + -1(2t + -2)

Remove parenthesis around (-1 + 2t2)
fx + -1gx = -1 + 2t2 + -1(2t + -2)

Reorder the terms:
fx + -1gx = -1 + 2t2 + -1(-2 + 2t)
fx + -1gx = -1 + 2t2 + (-2 * -1 + 2t * -1)
fx + -1gx = -1 + 2t2 + (2 + -2t)

Reorder the terms:
fx + -1gx = -1 + 2 + -2t + 2t2

Combine like terms: -1 + 2 = 1
fx + -1gx = 1 + -2t + 2t2

Solving
fx + -1gx = 1 + -2t + 2t2

Solving for variable 'f'.

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

Add 'gx' to each side of the equation.
fx + -1gx + gx = 1 + -2t + gx + 2t2

Combine like terms: -1gx + gx = 0
fx + 0 = 1 + -2t + gx + 2t2
fx = 1 + -2t + gx + 2t2

Reorder the terms:
fx = 1 + gx + -2t + 2t2

Divide each side by 'x'.
f = x-1 + g + -2tx-1 + 2t2x-1

Simplifying
f = x-1 + g + -2tx-1 + 2t2x-1

Reorder the terms:
f = g + -2tx-1 + 2t2x-1 + x-1

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