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Question

# Simplify. Identify any x-values for which the expression is undefined.$\frac { 6 x ^ { 3 } + 6 x } { x ^ { 2 } + 1 }$

Solution

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\begin{align*}\dfrac{6\cdot x^3+6\cdot x}{x^2+1} &=\dfrac{6\cdot x\cdot x^2+6\cdot x\cdot 1}{x^2+1} \\ &=\dfrac{6\cdot x\cdot \cancel{(x^2+1)}}{\cancel{x^2+1}} \tag{ factore out 6\cdot x in numerator}\\ &={\color{#4257b2} 6\cdot x} \tag{ cancel x^2 +1} \end{align*}

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