Evaluate
\frac{4x^{3}+6x^{2}-57x-24}{x\left(x-12\right)}
Expand
\frac{4x^{3}+6x^{2}-57x-24}{x\left(x-12\right)}
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\frac{\left(4x^{2}+x+1\right)x}{x\left(x-12\right)}+\frac{\left(5x+2\right)\left(x-12\right)}{x\left(x-12\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-12 and x is x\left(x-12\right). Multiply \frac{4x^{2}+x+1}{x-12} times \frac{x}{x}. Multiply \frac{5x+2}{x} times \frac{x-12}{x-12}.
\frac{\left(4x^{2}+x+1\right)x+\left(5x+2\right)\left(x-12\right)}{x\left(x-12\right)}
Since \frac{\left(4x^{2}+x+1\right)x}{x\left(x-12\right)} and \frac{\left(5x+2\right)\left(x-12\right)}{x\left(x-12\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{3}+x^{2}+x+5x^{2}-60x+2x-24}{x\left(x-12\right)}
Do the multiplications in \left(4x^{2}+x+1\right)x+\left(5x+2\right)\left(x-12\right).
\frac{4x^{3}+6x^{2}-57x-24}{x\left(x-12\right)}
Combine like terms in 4x^{3}+x^{2}+x+5x^{2}-60x+2x-24.
\frac{4x^{3}+6x^{2}-57x-24}{x^{2}-12x}
Expand x\left(x-12\right).
\frac{\left(4x^{2}+x+1\right)x}{x\left(x-12\right)}+\frac{\left(5x+2\right)\left(x-12\right)}{x\left(x-12\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-12 and x is x\left(x-12\right). Multiply \frac{4x^{2}+x+1}{x-12} times \frac{x}{x}. Multiply \frac{5x+2}{x} times \frac{x-12}{x-12}.
\frac{\left(4x^{2}+x+1\right)x+\left(5x+2\right)\left(x-12\right)}{x\left(x-12\right)}
Since \frac{\left(4x^{2}+x+1\right)x}{x\left(x-12\right)} and \frac{\left(5x+2\right)\left(x-12\right)}{x\left(x-12\right)} have the same denominator, add them by adding their numerators.
\frac{4x^{3}+x^{2}+x+5x^{2}-60x+2x-24}{x\left(x-12\right)}
Do the multiplications in \left(4x^{2}+x+1\right)x+\left(5x+2\right)\left(x-12\right).
\frac{4x^{3}+6x^{2}-57x-24}{x\left(x-12\right)}
Combine like terms in 4x^{3}+x^{2}+x+5x^{2}-60x+2x-24.
\frac{4x^{3}+6x^{2}-57x-24}{x^{2}-12x}
Expand x\left(x-12\right).
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