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f(x)=(2x-3)/(x^(3)+3x)

f(x)=2x−3x3+3x f(x)=\frac{2 x-3}{x^{3}+3 x}

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Full solution

Q. f(x)=2x−3x3+3x f(x)=\frac{2 x-3}{x^{3}+3 x}
  1. Identify expression and factor: Identify the expression and factor the denominator if possible. \newlinef(x)=2x−3x3+3xf(x) = \frac{2x - 3}{x^3 + 3x}\newline=2x−3x(x2+3)= \frac{2x - 3}{x(x^2 + 3)}
  2. Check for common factors: Check for common factors in the numerator and the denominator.\newlineNo common factors between (2x−3)(2x - 3) and x(x2+3)x(x^2 + 3).
  3. Simplify expression: Simplify the expression by reducing any common terms.\newlineSince there are no common factors, the expression remains:\newlinef(x)=2x−3x(x2+3)f(x) = \frac{2x - 3}{x(x^2 + 3)}

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