Giải các bất phương trình sau :
a) \(4x-8\ge3\left(3x-1\right)-2x+1\)
b) \(\left(x-3\right)\left(x+2\right)+\left(x+4\right)^2\le2x\left(x+5\right)+4\)
c) \(3x-\dfrac{x+2}{3}\le\dfrac{3\left(x-2\right)}{2}+5-x\)
d) \(x-\dfrac{x+2}{3}\ge3x-1+\dfrac{x}{2}\)
e) \(\dfrac{x\left(x+2\right)}{3}+\dfrac{\left(x-1\right)\left(x+2\right)}{2}\ge\dfrac{5\left(x+1\right)^2}{6}+1\)
f) \(\dfrac{x+5}{2012}+\dfrac{x+6}{2011}+\dfrac{x+7}{2010}>-3\)
Giải các phương trình sau :
a)\(\dfrac{5x+2}{6}\)\(-\dfrac{8x-1}{3}=\dfrac{4x+2}{5}-5\)
b)\(\dfrac{x+2}{x-2}-\dfrac{1}{x}=\dfrac{2}{x\left(x-2\right)}\)
c)\(2x^3 +6x^2=x^2+3x\)
d)\(\left|x-4\right|+3x=5\)
Thực hiện phép tính
\(a,\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
\(b,\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
\(c,\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
\(d,\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
\(e,\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
\(f,\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
\(g,\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
\(h,\dfrac{x^3}{x-1}-\dfrac{x^2}{x+1}-\dfrac{1}{x-1}+\dfrac{1}{x+1}\)
Tìm điều kiện xác định và rút gọn các biểu thức sau :
a/ \(A=\left(\dfrac{\sqrt{3}}{x^2+x\sqrt{3}+3}+\dfrac{3}{x^3-\sqrt{27}}\right).\left(\dfrac{x}{\sqrt{3}}+\dfrac{\sqrt{3}}{x}+1\right)\)
b/ \(B=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}-\dfrac{x^2+\sqrt{x}}{x-\sqrt{x}+1}+x+1\)
c/ \(C=\left(\dfrac{2+\sqrt{x}}{x+2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\right).\dfrac{x\sqrt{x}+x-\sqrt{x}-1}{\sqrt{x}}\)
d/ \(\left[\dfrac{1}{x-1}+\dfrac{x^2+1-2x}{\left(x-1\right)^2+3x}-\dfrac{1+4x-2x^2}{x^3-1}\right]:\dfrac{2}{x^2+1}\)
Cho biểu thức \(A=\dfrac{x^2+x}{x^2-2x+1}:\left(\dfrac{x+1}{x}-\dfrac{1}{1-x}+\dfrac{2-x^2}{x^2-x}\right)\)
a) Rút gọn \(A\)
b) Tính \(A\) biết \(\left|x-3\right|=2\)
c) Tìm \(x\) để \(A=\dfrac{1}{2}\)
d) Tìm \(x\) để \(A>1\)
e) Tìm \(x\) nguyên để \(A\) có giá trị nguyên
f) Với \(x>1\). Tìm giá trị nhỏ nhất của \(A\).
1. a) Tính 2x( 3x2+4xy )
b) Tìm x biết: x( x -1) + x - 1=0
c) Phân tích đa thức sau thành nhân tử: x2- xy - 3x +3y
2. Tính:
a) (x3+ 4x2+ x - 2) \(\div\) (x + 1)
b) \(\dfrac{x-3}{2x-2}+\dfrac{1}{x-1}\)
3. Tính:
\(\dfrac{1}{\left(x-y\right)\left(y-z\right)}+\dfrac{1}{\left(y-z\right)\left(z-x\right)}+\dfrac{1}{\left(z-x\right)\left(x-y\right)}\)
giúp mik vs ạ, cảm ơn nhìu!
\(x:\dfrac{x-1}{2}-\dfrac{x^3+3x\left(x-1\right)-1}{2x^2 +2x}.\dfrac{-4x}{x^2+1-2x}-\dfrac{4x^2}{x^2-1}\)
1, Tìm x biết: \(\dfrac{2}{x-1}>1\)
2, Rút gọn: \(A=\left(\dfrac{2+x}{2-x}+\dfrac{4x^2}{x^2-4}-\dfrac{2-x}{2+x}\right):\dfrac{x^2-3x}{2x^2-x^3}\)
a \(x^2-x=0\) b \(x^2-2x=0\) c (x+1)(x+2)=(2-x)(x+2)
d \(\dfrac{1}{x-2}+3=\dfrac{3-x}{x-2}\) đ \(\dfrac{8-x}{x-7}-8=\dfrac{1}{x-7}\)
e \(\dfrac{x}{2\left(x-3\right)}+\dfrac{x}{2\left(x+1\right)}=\dfrac{2x}{\left(x+1\right)\left(x-3\right)}\)
f \(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)
g \(\dfrac{90}{x}-\dfrac{36}{x-6}=2\) h \(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\) i \(\dfrac{x+3}{x-3}-\dfrac{1}{x}=\dfrac{3}{x\left(x-3\right)}\)
k \(\dfrac{3}{x+2}-\dfrac{2}{x-2}+\dfrac{8}{x^2-4}=0\) l \(\dfrac{3}{x+2}-\dfrac{2}{x-3}=\dfrac{8}{\left(x-3\right)\left(x+2\right)}\)
m\(\dfrac{x}{2x+6}-\dfrac{x}{2x+2}=\dfrac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
n \(\dfrac{x}{x+1}-\dfrac{2x-3}{1-x}=\dfrac{3x^2+5}{x^2-1}\) j \(\dfrac{5}{x+7}+\dfrac{8}{2x+14}=\dfrac{3}{2}\)
q \(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
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