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Find the square root of $$x^2+10+\frac{(-20x-15)}{x^2+4x+4}$$

I tried to do by taking the denominator across the entire expression, because the denominator was already a perfect square, but I ended up with an expression in the numerator which had no real roots: $$\frac{x^4+4x^3+14x^2+20x+25}{x^2+4x+4}$$

Is there a simpler method which I am missing? Thanks for any help :-)

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  • $\begingroup$ @Bernard, you are right, I didn't think about that! I have edited it $\endgroup$ – Fasal123 Apr 8 '18 at 11:43
  • $\begingroup$ But it has a root easily explicit. $\endgroup$ – Piquito Apr 8 '18 at 11:47
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$(x^2+ax+5)^2=x^4+2ax^3+(a^2+10)x+10ax+25=x^4+4x^3+14x^2+20x+25$ when $a=2$.

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