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\(P=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{2x+\sqrt{x}}{\sqrt{x}}+\frac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\frac{\sqrt{x}\left(2\sqrt{x}+1\right)}{\sqrt{x}}+\frac{2\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\left(2\sqrt{x}+1\right)+2\left(\sqrt{x}+1\right)\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-2\sqrt{x}-1+2\sqrt{x}+2\)
\(=\frac{x^2-\sqrt{x}}{x+\sqrt{x}+1}+1\)
\(=\frac{x^2-\sqrt{x}+x+\sqrt{x}+1}{x+\sqrt{x}+1}\)
\(=\frac{x^2+x+1}{x+\sqrt{x}+1}\)
\(B=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{a-\sqrt{a}}\right):\left(\frac{1}{\sqrt{a}+1}-\frac{2}{a-1}\right)\)
\(=\left(\frac{\sqrt{a}}{\sqrt{a}-1}-\frac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}\right):\left(\frac{1}{\sqrt{a}+1}-\frac{2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\right)\)
\(=\frac{a-1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\frac{1\left(\sqrt{a}-1\right)-2}{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}\)
\(=\frac{\left(\sqrt{a}+1\right)}{\sqrt{a}}.\frac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)}{\sqrt{a}-1-2}\)
\(=\frac{\left(\sqrt{a}+1\right)\left(a-1\right)}{\sqrt{a}\left(\sqrt{a}-3\right)}\)
\(A=\frac{\sqrt{x}-1}{x^2-x}:\left(\frac{1}{\sqrt{x}}-\frac{1}{\sqrt{x}+1}\right)\)
\(A=\frac{\sqrt{x}-1}{x\left(x-1\right)}:\left(\frac{\sqrt{x}+1-1}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)
\(A=\frac{1}{x\left(\sqrt{x}+1\right)}:\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\)
\(A=\frac{1}{x\left(\sqrt{x}+1\right)}.\left(\sqrt{x}+1\right)\)
\(A=\frac{1}{x}\)
A = x 2 − x x − 1 : x 1 − x + 1 1 A = x x − 1 x − 1 : x x + 1 x + 1 − 1 A = x x + 1 1 : x x + 1 x A = x x + 1 1 . x + 1 A = x 1 √ ( √ √ ) √ ( ) ( √ √ (√ ) ) (√ ) √ √ (√ ) (√ ) (√ )
A = x 2 − x x − 1 : x 1 − x + 1 1 A = x x − 1 x − 1 : x x + 1 x + 1 − 1 A = x x + 1 1 : x x + 1 x A = x x + 1 1 . x + 1 A = x 1 √ ( √ √ ) √ ( ) ( √ √ (√ ) ) (√ ) √ √ (√ ) (√ ) (√ )\(A = x 2 − x x − 1 : x 1 − x + 1 1 A = x x − 1 x − 1 : x x + 1 x + 1 − 1 A = x x + 1 1 : x x + 1 x A = x x + 1 1 . x + 1 A = x 1 √ ( √ √ ) √ ( ) ( √ √ (√ ) ) (√ ) √ √ (√ ) (√ ) (√ )\)
\(A=\left(a-1\right)\sqrt{\frac{a}{a-1}}+\sqrt{a\left(a-1\right)}-a\sqrt{\frac{a-1}{a}}\)
\(A=\sqrt{\left(a-1\right)^2.\frac{a}{a-1}}+\sqrt{a\left(a-1\right)}-\sqrt{a^2.\frac{a-1}{a}}\)
\(A=\sqrt{\left(a-1\right)a}+\sqrt{a\left(a-1\right)}-\sqrt{a\left(a-1\right)}\)
\(A=\sqrt{a\left(a-1\right)}\)
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