P = \(\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}+\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\)
P = \(\frac{\sqrt{x}-4x-1+4x}{1-4x}:\left(\frac{1+2x-2\sqrt{x}\left(2\sqrt{x}+1\right)-1+4x}{1-4x}\right)\)
P = \(\frac{\sqrt{x}-1}{1-4x}\cdot\frac{1-4x}{1+2x-4x-2\sqrt{x}-1+4x}\)
P = \(\frac{\sqrt{x}-1}{2x-2\sqrt{x}}\)
P = \(\frac{\sqrt{x}-1}{2\sqrt{x}\left(\sqrt{x}-1\right)}=\frac{1}{2\sqrt{x}}\)
Bài 1: giải ft
a)\(\frac{1}{x\left(x+2\right)}-\frac{1}{\left(x+1\right)^2}=\frac{1}{2}\)
b)\(\sqrt{4x^2-x+4}=3x+2\)
c)\(\sqrt{x^2-2x+5}=x^2-2x-1\)
d)\(\sqrt{8+\sqrt{x}}+\sqrt{5-\sqrt{x}}=5\)
e)\(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
Bài 2:Tìm nghiệm của ft
a)x+xy+y=9
b)\(x^2+xy+y^2=x^2y^2\)
Bài 3:Cho A=\(\left(\frac{\sqrt{x}-4x}{1-4x}-1\right):\left(\frac{1+2x}{1-4x}-\frac{2\sqrt{x}}{2\sqrt{x}-1}-1\right)\)
a)Rút gọn A
b)Tìm x để A>A^2
c)Tìm x để /A/=1/4
Rút gọn: P= \(\left(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{x}}\right):\left(\frac{2x+\sqrt{x}-1}{1-x}+\frac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}\right)\)
Rút gọn:
\(A=1-\left[\dfrac{2x\sqrt{x}+x-\sqrt{x}}{1+x\sqrt{x}}+\dfrac{2x-1+\sqrt{x}}{1-x}\right]\cdot\left[\dfrac{\left(x-\sqrt{x}\right)\left(1-\sqrt{x}\right)}{2\sqrt{x}-1}\right]\)
\(B=\left[1:\frac{2x-1}{x-x^2}\right]\cdot\left[\frac{2x^3+x^2-x}{x^3-1}-2-\frac{1}{x-1}\right]\)
Rút gọn biểu thức sau: A=\(\left[\left(x^4-x+\frac{x-3}{x^3+1}\right).\frac{\left(x^3-2x^2+2x-1\right)\left(x+1\right)}{x^9+x^7-3x^2-3}+1-\frac{2\left(x+6\right)}{x^2+1}\right].\frac{4x^2+4x+1}{\left(x+4\right)\left(3-x\right)}\)
Rút gọn biểu thức
1)\(\frac{c\left(a+c\right)-a\left(a-c\right)}{\frac{c}{a-c}-\frac{a}{a+ c}}\)
2) \(\frac{\frac{x^2-y^2}{x}}{\frac{1}{x}-\frac{1}{y}}\)
3) \(x:\frac{x-1}{2}-\frac{\left(x-1\right)\left(x^2+4x+1\right)}{2x^2+2x}.\frac{-4x}{\left(x-1\right)^2}-\frac{4x^2}{x^2-1}\)
Giải phương trình :
1)\(\sqrt[3]{6x+1}=8x^3-4x-1\\ \)
2)\(2x+\frac{x-1}{x}=\sqrt[2]{1-\frac{1}{x}}+3\sqrt{x-\frac{1}{x}}\)
3)\(\frac{15}{2}\left(30x^2-4x\right)=2004\left(\sqrt{30060x+1}+1\right)\)
Ai biết giải giúp mình nha,mình nổ não lun mà ko giải được.
Rút gọn biểu thức:
\(\left(\frac{2x+1}{\sqrt{x^3-1}}-\frac{\sqrt{x}}{x+\sqrt{x}+1}\right).\left(\frac{1+\sqrt{x^3}}{1+\sqrt{x}}-\sqrt{x}\right)\)
Giải \(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{2x+3}}=\sqrt{3}.\left(\frac{1}{\sqrt{4x}-3}+\frac{1}{\sqrt{5x}-6}\right)\)
Giải phương trình:
a) \(\sqrt{3x-2}=-4x^2+21x-22\)
b) \(\left(x-\frac{1}{2}\right)\sqrt{1+x}+\left(x+\frac{1}{2}\right)\sqrt{1-x}=x\)
c) \(2x^3+x^2+x=\left(x^2+6x+6\right)\sqrt{x+1}\)
