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Expression simplification/ Fraction Decomposition into the simple/ sqrt(((x+1)*(x-4)^2)/(((x+2)*(3-x))))

How do you sqrt(((x+1)*(x-4)^2)/(((x+2)*(3-x)))) in partial fractions?

An expression to simplify:

The solution

You have entered [src] 
     __________________
    /                2 
   /  (x + 1)*(x - 4)  
  /   ---------------- 
\/    (x + 2)*(3 - x)
$$\sqrt{\frac{\left(x - 4\right)^{2} \left(x + 1\right)}{\left(3 - x\right) \left(x + 2\right)}}$$ 
sqrt(((x + 1)*(x - 4)^2)/(((x + 2)*(3 - x))))
Fraction decomposition [src] 
sqrt(16/(6 + x - x^2) + x^3/(6 + x - x^2) - 7*x^2/(6 + x - x^2) + 8*x/(6 + x - x^2))
$$\sqrt{\frac{x^{3}}{- x^{2} + x + 6} - \frac{7 x^{2}}{- x^{2} + x + 6} + \frac{8 x}{- x^{2} + x + 6} + \frac{16}{- x^{2} + x + 6}}$$ 
      ___________________________________________________
     /                   3             2                 
    /      16           x           7*x          8*x     
   /   ---------- + ---------- - ---------- + ---------- 
  /             2            2            2            2 
\/     6 + x - x    6 + x - x    6 + x - x    6 + x - x
General simplification [src] 
     _____________________
    /          2          
   /  -(-4 + x) *(1 + x)  
  /   ------------------- 
\/      (-3 + x)*(2 + x)
$$\sqrt{- \frac{\left(x - 4\right)^{2} \left(x + 1\right)}{\left(x - 3\right) \left(x + 2\right)}}$$ 
sqrt(-(-4 + x)^2*(1 + x)/((-3 + x)*(2 + x)))
Numerical answer [src] 
4.0*((-1 + 0.25*x)^2*(1.0 + x)/((2.0 + x)*(3.0 - x)))^0.5
4.0*((-1 + 0.25*x)^2*(1.0 + x)/((2.0 + x)*(3.0 - x)))^0.5
Expand expression [src] 
    _______    __________     _______          
   /   1      /        2     /   1      _______
  /  ----- *\/  (x - 4)  *  /  ----- *\/ x + 1 
\/   3 - x                \/   x + 2
$$\sqrt{x + 1} \sqrt{\frac{1}{3 - x}} \sqrt{\left(x - 4\right)^{2}} \sqrt{\frac{1}{x + 2}}$$ 
sqrt(1/(3 - x))*sqrt((x - 4)^2)*sqrt(1/(x + 2))*sqrt(x + 1)
Combinatorics [src] 
      ___________________
     /         2         
    /  (-4 + x) *(1 + x) 
   /   ----------------- 
  /                 2    
\/         6 + x - x
$$\sqrt{\frac{\left(x - 4\right)^{2} \left(x + 1\right)}{- x^{2} + x + 6}}$$ 
sqrt((-4 + x)^2*(1 + x)/(6 + x - x^2))
Common denominator [src] 
      ___________________________________________________
     /                   3             2                 
    /      16           x           7*x          8*x     
   /   ---------- + ---------- - ---------- + ---------- 
  /             2            2            2            2 
\/     6 + x - x    6 + x - x    6 + x - x    6 + x - x
$$\sqrt{\frac{x^{3}}{- x^{2} + x + 6} - \frac{7 x^{2}}{- x^{2} + x + 6} + \frac{8 x}{- x^{2} + x + 6} + \frac{16}{- x^{2} + x + 6}}$$ 
sqrt(16/(6 + x - x^2) + x^3/(6 + x - x^2) - 7*x^2/(6 + x - x^2) + 8*x/(6 + x - x^2))
Rational denominator [src] 
      ___________________
     /         2         
    /  (-4 + x) *(1 + x) 
   /   ----------------- 
  /                 2    
\/         6 + x - x
$$\sqrt{\frac{\left(x - 4\right)^{2} \left(x + 1\right)}{- x^{2} + x + 6}}$$ 
sqrt((-4 + x)^2*(1 + x)/(6 + x - x^2))
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