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Simplifying (f + -1g)(x) = 0 Reorder the terms for easier multiplication: x(f + -1g) = 0 (f * x + -1g * x) = 0 (fx + -1gx) = 0 Solving fx + -1gx = 0 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 = 0 + gx Combine like terms: -1gx + gx = 0 fx + 0 = 0 + gx fx = 0 + gx Remove the zero: fx = gx Divide each side by 'x'. f = g Simplifying f = g
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