Final answer to the problem
$\frac{\sqrt{x+3}\left(\sqrt{6-2x}-\sqrt{9-x}\right)}{-3-2x+x}$
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Step-by-step Solution
Learn how to solve factor by difference of squares problems step by step online. Rationalize and simplify the expression ((x+3)^(1/2))/((6-2x)^(1/2)+(9-x)^(1/2)). Multiply and divide the fraction \frac{\sqrt{x+3}}{\sqrt{6-2x}+\sqrt{9-x}} by the conjugate of it's denominator \sqrt{6-2x}+\sqrt{9-x}. Multiplying fractions \frac{\sqrt{x+3}}{\sqrt{6-2x}+\sqrt{9-x}} \times \frac{\sqrt{6-2x}-\sqrt{9-x}}{\sqrt{6-2x}-\sqrt{9-x}}. Solve the product of difference of squares \left(\sqrt{6-2x}+\sqrt{9-x}\right)\left(\sqrt{6-2x}-\sqrt{9-x}\right).
Final answer to the problem
$\frac{\sqrt{x+3}\left(\sqrt{6-2x}-\sqrt{9-x}\right)}{-3-2x+x}$
