bài 1: Rút gọn các biểu thức sau
a) A=\(\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{\left(\sqrt{x}\right)^2+\sqrt{x}}\right)\dfrac{\sqrt{x}}{\sqrt{x}-1}\) với x > 0 và x≠1
b) B=\(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\) với a > 0; a≠1;a≠4
c) C=\(\left(\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\right):\dfrac{\sqrt{x}}{\sqrt{x}+1}\) với x > 0;x≠1
d) D=\(\left(\dfrac{2}{x-4}+\dfrac{1}{\sqrt{x}+2}\right):\dfrac{1}{\sqrt{x}+2}\) với x≥0;x≠4
e) E=\(\dfrac{x}{\sqrt{x}-1}+\dfrac{\sqrt{x}-2x}{x-\sqrt{x}}\) với x > 0;x ≠ 1
f) F=\(\left(\dfrac{\sqrt{x}}{\sqrt{x}+3}+\dfrac{3}{\sqrt{x}-3}\right).\dfrac{\sqrt{x}+3}{x+9}\) với x ≥ 0;x ≠ 9
giúp với ạ
a) \(A=\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{1}{\left(\sqrt{x}\right)^2+\sqrt{x}}\right)\dfrac{\sqrt{x}}{\sqrt{x}-1}\)
Với \(x>0\) và \(x\ne1\)
\(A=\dfrac{\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\dfrac{\sqrt{x}}{\left(x+\sqrt{x}\right)\left(\sqrt{x}-1\right)}\)
\(A=\dfrac{\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}-\dfrac{1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(A=\dfrac{\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\)
\(A=\dfrac{1}{\sqrt{x}+1}\)
b) \(B=\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)
Với \(a>0;a\ne1;a\ne4\)
\(B=\left[\dfrac{\sqrt{a}-\left(\sqrt{a}-1\right)}{\sqrt{a}\left(\sqrt{a}-1\right)}\right]:\left[\dfrac{\left(\sqrt{a}+1\right)\left(\sqrt{a}-1\right)-\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\right]\)
\(B=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}:\dfrac{a-1-\left(a-4\right)}{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}\)
\(B=\dfrac{1}{\sqrt{a}\left(\sqrt{a}-1\right)}.\dfrac{\left(\sqrt{a}-2\right)\left(\sqrt{a}-1\right)}{3}\)
\(B=\dfrac{\sqrt{a}-2}{3\sqrt{a}}\)
