\[\frac{{x}^{3}-12{x}^{2}-42}{{x}^{2}+x-3}\]
1
Polynomial Division: Divide x3−12x2−42{x}^{3}-12{x}^{2}-42 by x2+x−3{x}^{2}+x-3.

xx−13-13
x2+x−3x^2+x-3x3x^3−12x2-12x^2−42-42
x3x^3x2x^2−3x-3x
−13x2-13x^23x3x−42-42
−13x2-13x^2−13x-13x3939
16x16x−81-81

2
Rewrite the expression using the above.
x−13+16x−81x2+x−3x-13+\frac{16x-81}{{x}^{2}+x-3}

Done
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