Evaluate
\frac{-x^{2}+24x-13}{12x\left(x+1\right)}
Expand
-\frac{x^{2}-24x+13}{12x\left(x+1\right)}
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\frac{-13x^{2}+\left(12x+12\right)\left(x+1\right)-25}{12x\left(x+1\right)}
Combine 12x^{2} and -25x^{2} to get -13x^{2}.
\frac{-13x^{2}+12x^{2}+24x+12-25}{12x\left(x+1\right)}
Use the distributive property to multiply 12x+12 by x+1 and combine like terms.
\frac{-x^{2}+24x+12-25}{12x\left(x+1\right)}
Combine -13x^{2} and 12x^{2} to get -x^{2}.
\frac{-x^{2}+24x-13}{12x\left(x+1\right)}
Subtract 25 from 12 to get -13.
\frac{-x^{2}+24x-13}{12x^{2}+12x}
Use the distributive property to multiply 12x by x+1.
\frac{-13x^{2}+\left(12x+12\right)\left(x+1\right)-25}{12x\left(x+1\right)}
Combine 12x^{2} and -25x^{2} to get -13x^{2}.
\frac{-13x^{2}+12x^{2}+24x+12-25}{12x\left(x+1\right)}
Use the distributive property to multiply 12x+12 by x+1 and combine like terms.
\frac{-x^{2}+24x+12-25}{12x\left(x+1\right)}
Combine -13x^{2} and 12x^{2} to get -x^{2}.
\frac{-x^{2}+24x-13}{12x\left(x+1\right)}
Subtract 25 from 12 to get -13.
\frac{-x^{2}+24x-13}{12x^{2}+12x}
Use the distributive property to multiply 12x by x+1.
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