a: \(\frac14\sqrt2-\frac32\cdot\sqrt{4,5}+\frac25\cdot\sqrt{50}\)
\(=\frac14\sqrt2-\frac32\cdot\frac{3\sqrt2}{2}+\frac25\cdot5\sqrt2=\frac14\sqrt2+2\sqrt2-\frac94\sqrt2\)
=0
b: \(\left(\frac{\sqrt{x}-2}{x-1}-\frac{\sqrt{x}+2}{x+2\sqrt{x}+1}\right)\cdot\frac{x\sqrt{x}-x-\sqrt{x}+1}{\sqrt{x}}\)
\(=\frac{\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)-\left(\sqrt{x}+2\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\cdot\frac{x\left(\sqrt{x}-1\right)-\left(\sqrt{x}-1\right)}{\sqrt{x}}\)
\(=\frac{x-\sqrt{x}-2-\left(x+\sqrt{x}-2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)^2}\cdot\frac{\left(\sqrt{x}-1\right)^2\cdot\left(\sqrt{x}+1\right)}{\sqrt{x}}\)
\(=-\frac{2\sqrt{x}}{\sqrt{x}}\cdot\frac{\sqrt{x}-1}{\sqrt{x}+1}=\frac{-2\left(\sqrt{x}-1\right)}{\sqrt{x}+1}\)
