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Step-by-step Solution

Solve (/((xx^2-2x+6)^0.5-(x^2+2x+6)^0.5))/(x^2-4x+3)

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Answer

$\frac{}{\left(\sqrt{x^{3}-2x+6}-\sqrt{\left(x+1\right)^2+5}\right)\left(x-3\right)\left(x-1\right)}$

Step-by-step explanation

Problem to solve:

$\frac{\frac{}{\sqrt{x x^2-2x+6}-\sqrt{x^2+2x+6}}}{x^2-4x+3}$
1

When multiplying exponents with same base you can add the exponents

$\frac{\frac{}{\sqrt{x^{3}-2x+6}-\sqrt{x^2+2x+6}}}{x^2-4x+3}$
2

Simplifying the fraction

$\frac{}{\left(\sqrt{x^{3}-2x+6}-\sqrt{x^2+2x+6}\right)\left(x^2-4x+3\right)}$

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Answer

$\frac{}{\left(\sqrt{x^{3}-2x+6}-\sqrt{\left(x+1\right)^2+5}\right)\left(x-3\right)\left(x-1\right)}$

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$\frac{\frac{}{\sqrt{x x^2-2x+6}-\sqrt{x^2+2x+6}}}{x^2-4x+3}$

Main topic:

Completing the square

Time to solve it:

~ 0.7 seconds