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How do you (x^2-12)/(x-3)-x/(3-x) in partial fractions?

An expression to simplify:

The solution

You have entered [src]
 2             
x  - 12     x  
------- - -----
 x - 3    3 - x
$$- \frac{x}{3 - x} + \frac{x^{2} - 12}{x - 3}$$
(x^2 - 12)/(x - 3) - x/(3 - x)
Fraction decomposition [src]
4 + x
$$x + 4$$
4 + x
General simplification [src]
4 + x
$$x + 4$$
4 + x
Common denominator [src]
4 + x
$$x + 4$$
4 + x
Rational denominator [src]
/       2\                     
\-12 + x /*(3 - x) - x*(-3 + x)
-------------------------------
        (-3 + x)*(3 - x)       
$$\frac{- x \left(x - 3\right) + \left(3 - x\right) \left(x^{2} - 12\right)}{\left(3 - x\right) \left(x - 3\right)}$$
((-12 + x^2)*(3 - x) - x*(-3 + x))/((-3 + x)*(3 - x))
Combinatorics [src]
4 + x
$$x + 4$$
4 + x
Numerical answer [src]
(-12.0 + x^2)/(-3.0 + x) - x/(3.0 - x)
(-12.0 + x^2)/(-3.0 + x) - x/(3.0 - x)
Combining rational expressions [src]
/       2\                     
\-12 + x /*(3 - x) - x*(-3 + x)
-------------------------------
        (-3 + x)*(3 - x)       
$$\frac{- x \left(x - 3\right) + \left(3 - x\right) \left(x^{2} - 12\right)}{\left(3 - x\right) \left(x - 3\right)}$$
((-12 + x^2)*(3 - x) - x*(-3 + x))/((-3 + x)*(3 - x))