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\frac{2x^{2}+2x-\left(x^{2}+24\right)}{x+6}
Since \frac{2x^{2}+2x}{x+6} and \frac{x^{2}+24}{x+6} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}+2x-x^{2}-24}{x+6}
Do the multiplications in 2x^{2}+2x-\left(x^{2}+24\right).
\frac{x^{2}+2x-24}{x+6}
Combine like terms in 2x^{2}+2x-x^{2}-24.
\frac{\left(x-4\right)\left(x+6\right)}{x+6}
Factor the expressions that are not already factored in \frac{x^{2}+2x-24}{x+6}.
x-4
Cancel out x+6 in both numerator and denominator.
\frac{2x^{2}+2x-\left(x^{2}+24\right)}{x+6}
Since \frac{2x^{2}+2x}{x+6} and \frac{x^{2}+24}{x+6} have the same denominator, subtract them by subtracting their numerators.
\frac{2x^{2}+2x-x^{2}-24}{x+6}
Do the multiplications in 2x^{2}+2x-\left(x^{2}+24\right).
\frac{x^{2}+2x-24}{x+6}
Combine like terms in 2x^{2}+2x-x^{2}-24.
\frac{\left(x-4\right)\left(x+6\right)}{x+6}
Factor the expressions that are not already factored in \frac{x^{2}+2x-24}{x+6}.
x-4
Cancel out x+6 in both numerator and denominator.
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Limits
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