Ta có: \(\dfrac{20}{x}-\dfrac{20}{x+2}=\dfrac{10}{3}\)
Suy ra: \(10x\left(x+2\right)=60\left(x+2\right)-60x\)
\(\Leftrightarrow10x^2+20x-120=0\)
\(\Leftrightarrow x^2+2x-12=0\)
\(\Leftrightarrow\left(x+1\right)^2=13\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{13}-1\left(nhận\right)\\x=-\sqrt{13}-1\left(nhận\right)\end{matrix}\right.\)
Giai các ptr sau
a,\(\dfrac{1}{x-1}-\dfrac{3x^2}{x^3-1}=\dfrac{2x}{x^2+x+1}\)
b,\(\dfrac{8800}{x-2}-\dfrac{8800}{x}=20\)
c,\(\dfrac{1}{x}+\dfrac{1}{x+5}=\dfrac{1}{6}\)
d,\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
a : \(\dfrac{3}{\sqrt{x}-5}+\dfrac{20-2\sqrt{x}}{x-25}\)với x ≥ 0 x ≠ 25
b : \(\dfrac{\sqrt{x}}{\sqrt{x}-3}+\dfrac{2\sqrt{x}-2}{x-9}\)với x ≥ 0 x ≠ 9
c : \(\dfrac{\sqrt{x}-1}{\sqrt{x}+2}+\dfrac{5\sqrt{x}-2}{x-4}\)với x ≥ 0 x ≠ 4
d : \(\left(\dfrac{x-2}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}+2}\right).\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\)với ≥ 0 x ≠ 1
\(B=\dfrac{3}{\sqrt{x+5}}+\dfrac{20-2\sqrt{x}}{x-25}\)
4.
\(A=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}\right)-\left(\dfrac{1}{x+\sqrt{x}}\right).\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2}{x-1}\right)\)
a. Rút gọn A.
b. Tính x khi \(A=\dfrac{1}{2}\)
5. CMR
\(\left(\dfrac{\sqrt{30}}{\sqrt{3}}-\dfrac{\sqrt{20}}{\sqrt{2}}-\dfrac{6}{\sqrt{6}}\right).\sqrt{4+\sqrt{15}}=2\)
nhanh lên nha
\(\dfrac{60}{x}\)-\(\dfrac{60}{x+2}\)=\(\dfrac{1}{20}\)
a \(\sqrt{4x-20}+\sqrt{x-5}=4+3\sqrt{\dfrac{x-5}{9}}\)
b \(\sqrt{4x-20}+\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{4x-45}=4\)
a) \(\sqrt{4x^2-9}=2\sqrt{x+3}\)
b) \(\sqrt{4x+20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=4\)
c) \(\dfrac{2}{3}\sqrt{9x-9}-\dfrac{1}{4}\sqrt{16x-16}+27\sqrt{\dfrac{x-1}{81}}=4\)
d)\(5\sqrt{\dfrac{9x-27}{25}}-7\sqrt{\dfrac{4x-12}{9}}-7\sqrt{x^2-9}+18\sqrt{\dfrac{9x^2-81}{81}}=0\)
rút gọn
a)\(\sqrt{20}\)+\(\sqrt{80}\)-\(\sqrt{45}\)
b)4.\(\sqrt{\dfrac{2}{9}}\)+\(\sqrt{2}\)+\(\sqrt{\dfrac{1}{18}}\)
c)\(\dfrac{1}{\sqrt{3}-1}\)-\(\dfrac{1}{\sqrt{3}+1}\)
d)\(\dfrac{1}{\sqrt{x}-1}\)-\(\dfrac{1}{\sqrt{x}+1}\)+1
e)\(\sqrt{x}\)-2+\(\dfrac{10-x}{\sqrt{x}+2}\)
g)\(\dfrac{1}{\sqrt{x}+2}\)-\(\dfrac{2}{\sqrt{x}-2}\)-\(\dfrac{\sqrt{x}}{4-x}\)
b)\(\sqrt{4x-20}+\sqrt{x+5}-\dfrac{1}{3}\sqrt{9x-45}=4\)
c) \(\sqrt{\dfrac{3x-2}{x+1}}=3\)
d) \(\dfrac{\sqrt{5x-4}}{\sqrt{x+2}}=2\)
