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\frac{3x^{2}+4x-\left(27x+8\right)}{x-8}
Since \frac{3x^{2}+4x}{x-8} and \frac{27x+8}{x-8} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}+4x-27x-8}{x-8}
Do the multiplications in 3x^{2}+4x-\left(27x+8\right).
\frac{3x^{2}-23x-8}{x-8}
Combine like terms in 3x^{2}+4x-27x-8.
\frac{\left(x-8\right)\left(3x+1\right)}{x-8}
Factor the expressions that are not already factored in \frac{3x^{2}-23x-8}{x-8}.
3x+1
Cancel out x-8 in both numerator and denominator.
\frac{3x^{2}+4x-\left(27x+8\right)}{x-8}
Since \frac{3x^{2}+4x}{x-8} and \frac{27x+8}{x-8} have the same denominator, subtract them by subtracting their numerators.
\frac{3x^{2}+4x-27x-8}{x-8}
Do the multiplications in 3x^{2}+4x-\left(27x+8\right).
\frac{3x^{2}-23x-8}{x-8}
Combine like terms in 3x^{2}+4x-27x-8.
\frac{\left(x-8\right)\left(3x+1\right)}{x-8}
Factor the expressions that are not already factored in \frac{3x^{2}-23x-8}{x-8}.
3x+1
Cancel out x-8 in both numerator and denominator.
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