Question

\(\left(\frac{x-3\sqrt{x}}{x-9}-1\right):\left(\frac{9-x}{x+\sqrt{x}-6}-\frac{\sqrt{x}-3}{\sqrt{x}-2}-\frac{\sqrt{x}-2}{\sqrt{x}+3}\right)\)

\(\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}-\frac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)

\(\left(\frac{2\sqrt{x}+x}{x\sqrt{x}-1}-\frac{1}{\sqrt{x}+1}\right):\left(1-\frac{\sqrt{x}+2}{x+\sqrt{x}+1}\right)\)

\(\frac{\sqrt{x}+2}{\sqrt{x}+3}-\frac{5}{x+\sqrt{x}-6}+\frac{1}{2-\sqrt{x}}\)

Answer 1

c) \(C=\frac{\left(2\sqrt{x}+x\right)\left(\sqrt{x}+1\right)-\left(x\sqrt{x}-1\right)}{\left(x\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}:\frac{x+\sqrt{x}+1-\left(\sqrt{x}+2\right)}{x+\sqrt{x}+1}=\)

\(C=\frac{x\sqrt{x}+2x+x+2\sqrt{x}-x\sqrt{x}+1}{\left(\left(\sqrt{x}\right)^3-1\right)\left(\sqrt{x}+1\right)}\times\frac{x+\sqrt{x}+1}{x-1}=\)

\(C=\frac{3x+2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)\left(\sqrt{x}+1\right)}\times\frac{x+\sqrt{x}+1}{x-1}=\)

\(C=\frac{3x+2\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\times\frac{1}{x-1}=\)

\(C=\frac{3x+2\sqrt{x}+1}{x-1}\times\frac{1}{x-1}=\frac{3x+2\sqrt{x}+1}{\left(x-1\right)^2}.\)

Answer 2

các bạn giúp mình  với 

Answer 3

d) ĐK: x>=0; x khác 4.

\(D=\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)-5-\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}.\)

\(D=\frac{x-4-5-\sqrt{x}-3}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\frac{x-\sqrt{x}-12}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}=\frac{\left(\sqrt{x}+3\right)\left(\sqrt{x}-4\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(D=\frac{\sqrt{x}-4}{\sqrt{x}-2}\)

Answer 4

\(\frac{\sqrt{x}+2}{\sqrt{x}+3}-\frac{5}{x+\sqrt{x}-6}+\frac{1}{2-\sqrt{x}}\)

\(=\frac{\sqrt{x}+2}{\sqrt{x}+3}+\frac{5}{-x-\sqrt{x}+6}+\frac{1}{2-\sqrt{x}}\)

\(=\frac{\sqrt{x}+2}{\sqrt{x}+3}+\frac{5}{2\sqrt{x}-x+6-3\sqrt{x}}+\frac{1}{2-\sqrt{x}}\)

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

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

\(=\frac{\left(\sqrt{x}+2\right)\left(2-\sqrt{x}\right)}{\left(\sqrt{x+3}\right)\left(2-\sqrt{x}\right)}+\frac{5}{\left(\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}+\frac{\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}\)

\(=\frac{4-x+5+\sqrt{x}+3}{\left(\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}\)

\(=\frac{12-x+\sqrt{x}}{\left(\sqrt{x}+3\right)\left(2-\sqrt{x}\right)}\)

\(=\frac{-\left(12-x+\sqrt{x}\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{x-2.\frac{1}{2}\sqrt{x}+\frac{1}{4}-\frac{49}{4}}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}-\frac{1}{2}\right)^2-\left(\frac{7}{2}\right)^2}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}-\frac{1}{2}-\frac{7}{2}\right)\left(\sqrt{x}-\frac{1}{2}+\frac{7}{2}\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\left(\sqrt{x}-4\right)\left(\sqrt{x}+3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-2\right)}\)

\(=\frac{\sqrt{x}-4}{\sqrt{x}-2}\)