Question : Simplify the given expression $\frac{(x+3)^3+(x-3)^3}{x^2+27}$.
Option 1: $3x$
Option 2: $x$
Option 3: $4x$
Option 4: $2x$
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Correct Answer: $2x$
Solution :
Consider $\frac{(x+3)^3+(x-3)^3}{x^2+27}$
= $\frac{x^3+3^3+3\times x\times 3(x+3)+x^3-3^3-3\times x\times 3(x-3)}{}$
= $\frac{2x^3+9x(x+3)-9x(x-3)}{x^2+27}$
= $\frac{2x^3+9x^2+27x-9x^2+27x}{x^2+27}$
= $\frac{2x^3+2\times 27x}{x^2+27}$
= $\frac{2x(x^2+27)}{x^2+27}$
= $2x$
Hence, the correct answer is $2x$.
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