Violympic toán 8
Các câu hỏi tương tự
Tính:
\(a,\dfrac{x+3}{2x-1}-\dfrac{x^2-5}{4x^2-4x+1}-\dfrac{2x^3+5x^2-x-1}{8x^3-12x^2+6x-1}\)
\(b,\dfrac{1}{1-x}+\dfrac{1}{1+x}+\dfrac{2}{1+x^2}+\dfrac{4}{1+x^4}+\dfrac{8}{1+x^8}+\dfrac{16}{1+x^{16}}\)
Giải pt:
\(\dfrac{x^2+4x+6}{x+2}+\dfrac{x^2+16x+72}{x+8}=\dfrac{x^2+8x+20}{x+4}+\dfrac{x^2+12x+42}{x+6}\)
Giải PT sau:a, 3x - 7 0b, 8 - 5x 0c, 3x - 2 5x + 8d, dfrac{3x-2}{3} dfrac{1-x}{2}e, ( 5x + 1)(x - 3) 0f, (x + 1)(2x - 3) 0g, 4x(x + 3) - 5(x + 3) 0h, 8(x - 6) - 2x(6 - x) 0i, dfrac{2}{x-1} + dfrac{1}{x} dfrac{2x+5}{x^2-x}k, dfrac{3}{x+2} - dfrac{2}{x-2} dfrac{2-x}{x^2-4}m, dfrac{3}{x} - dfrac{2}{x-3} dfrac{4-x}{x^2-3}n,dfrac{3}{2x+10}+ dfrac{2x}{x^2-25} dfrac{3}{x-5}u, dfrac{2}{x+3} - dfrac{3}{x-2} dfrac{x+4}{left(x+3right)left(x-2right)}
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Giải PT sau:
a, 3x - 7 = 0
b, 8 - 5x = 0
c, 3x - 2 = 5x + 8
d, \(\dfrac{3x-2}{3}\) = \(\dfrac{1-x}{2}\)
e, ( 5x + 1)(x - 3) = 0
f, (x + 1)(2x - 3) = 0
g, 4x(x + 3) - 5(x + 3) = 0
h, 8(x - 6) - 2x(6 - x) = 0
i, \(\dfrac{2}{x-1}\) + \(\dfrac{1}{x}\) = \(\dfrac{2x+5}{x^2-x}\)
k, \(\dfrac{3}{x+2}\) - \(\dfrac{2}{x-2}\) = \(\dfrac{2-x}{x^2-4}\)
m, \(\dfrac{3}{x}\) - \(\dfrac{2}{x-3}\) = \(\dfrac{4-x}{x^2-3}\)
n,\(\dfrac{3}{2x+10}\)+ \(\dfrac{2x}{x^2-25}\) = \(\dfrac{3}{x-5}\)
u, \(\dfrac{2}{x+3}\) - \(\dfrac{3}{x-2}\) = \(\dfrac{x+4}{\left(x+3\right)\left(x-2\right)}\)
Giải các phương trình sau:
a) x^2+dfrac{2x}{x-1}8
b) dfrac{x^2+2x+1}{x^2+2x+2}+dfrac{x^2+2x+2}{x^2+2x+3}dfrac{7}{6}
c) dfrac{x+4}{x-1}+dfrac{x-4}{x+1}dfrac{x+8}{x-2}+dfrac{x-8}{x+2}+6
d) left(x^2+6x+8right)left(x^2+8x+15right)24
e) left(x^2+x-2right)left(x^2+9x+18right)28
f) 3left(-x^2+2x+3right)^4-26x^2left(-x^2+2x+3right)^2-9x^40
g) x^4+6x^3+11x^2+6x+10
h) left(x-3right)left(x-5right)left(x-6right)left(x-10right)-24x^20
i) left(x+2right)^4+left(x+8right)^4272
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Giải các phương trình sau:
a) \(x^2+\dfrac{2x}{x-1}=8\)
b) \(\dfrac{x^2+2x+1}{x^2+2x+2}+\dfrac{x^2+2x+2}{x^2+2x+3}=\dfrac{7}{6}\)
c) \(\dfrac{x+4}{x-1}+\dfrac{x-4}{x+1}=\dfrac{x+8}{x-2}+\dfrac{x-8}{x+2}+6\)
d) \(\left(x^2+6x+8\right)\left(x^2+8x+15\right)=24\)
e) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)=28\)
f) \(3\left(-x^2+2x+3\right)^4-26x^2\left(-x^2+2x+3\right)^2-9x^4=0\)
g) \(x^4+6x^3+11x^2+6x+1=0\)
h) \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2=0\)
i) \(\left(x+2\right)^4+\left(x+8\right)^4=272\)
Giải các phương trình sau:
1. \(a,\dfrac{6}{x-1}-\dfrac{4}{x-3}=\dfrac{8}{2x-6}\)
\(b,\dfrac{1}{x-2}+\dfrac{5}{x+1}=\dfrac{3}{2-x}\)
\(c,\dfrac{3x}{x-2}-\dfrac{x}{x-5}=\dfrac{3x}{\left(x-2\right)\left(5-x\right)}\)
2. \(a,\left(x+2\right)\left(3-4x\right)=x^2+4x+4\)
\(b,2x^2-6x+1\)
4.Giải phương trình
a) dfrac{x+5}{x-5}-dfrac{x-5}{x+5}dfrac{20}{x^2-25}
b)dfrac{1}{x-1}+dfrac{2}{x+1}dfrac{x}{x^2-1}
c)5+dfrac{76}{x^2-16}dfrac{2x-1}{x+4}-dfrac{3x-1}{4-x}
d)dfrac{90}{x}-dfrac{36}{x-6}2
e)dfrac{1}{x}+dfrac{1}{x+10}dfrac{1}{12}
f)dfrac{x+3}{x-3}-dfrac{1}{x}dfrac{3}{xleft(x-3right)}
g)dfrac{3}{x+2}-dfrac{2}{x-2}+dfrac{8}{x^2-4}0
h)dfrac{3}{x+2}-dfrac{2}{x-3}dfrac{8}{left(x-3right)left(x+2right)}
i)dfrac{x}{2x+6}-dfrac{x}{2x+2}dfrac{3x+2}{left(x+1right)left(x+3right)}
k)d...
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4.Giải phương trình
a) \(\dfrac{x+5}{x-5}-\dfrac{x-5}{x+5}=\dfrac{20}{x^2-25}\)
b)\(\dfrac{1}{x-1}+\dfrac{2}{x+1}=\dfrac{x}{x^2-1}\)
c)\(5+\dfrac{76}{x^2-16}=\dfrac{2x-1}{x+4}-\dfrac{3x-1}{4-x}\)
d)\(\dfrac{90}{x}-\dfrac{36}{x-6}=2\)
e)\(\dfrac{1}{x}+\dfrac{1}{x+10}=\dfrac{1}{12}\)
f)\(\dfrac{x+3}{x-3}-\dfrac{1}{x}=\dfrac{3}{x\left(x-3\right)}\)
g)\(\dfrac{3}{x+2}-\dfrac{2}{x-2}+\dfrac{8}{x^2-4}=0\)
h)\(\dfrac{3}{x+2}-\dfrac{2}{x-3}=\dfrac{8}{\left(x-3\right)\left(x+2\right)}\)
i)\(\dfrac{x}{2x+6}-\dfrac{x}{2x+2}=\dfrac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
k)\(\dfrac{x}{x+1}-\dfrac{2x-3}{1-x}=\dfrac{3x^2+5}{x^2-1}\)
l)\(\dfrac{5}{x+7}+\dfrac{8}{2x+14}=\dfrac{3}{2}\)
m)\(\dfrac{x-1}{x}-\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
Cần gấp ạ
thực hiên phép tính
a.\(\dfrac{x^2+y^2}{4\left(x+y\right)}+\dfrac{2xy}{4\left(x+y\right)}\)
b.\(\dfrac{x+5}{2x-2}-\dfrac{4}{x^2-1}:\dfrac{2}{x+1}\)
Thực hiện phép tính:
a) dfrac{x+1}{x+2}:left(dfrac{x+2}{x+3}:dfrac{x+3}{x+1}right)
b, dfrac{8}{left(x^2+3right)left(x^2-1right)}+dfrac{2}{x^2+3}+dfrac{1}{x+1}
c, dfrac{x+y}{2left(x-yright)}-dfrac{x-y}{2left(x+yright)}+dfrac{2y^2}{x^2-y^2}
d,dfrac{x-1}{x^3}-dfrac{x+1}{x^3-x^2}+dfrac{3}{x^3-2x^2+x}
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Thực hiện phép tính:
a) \(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
b, \(\dfrac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\dfrac{2}{x^2+3}+\dfrac{1}{x+1}\)
c, \(\dfrac{x+y}{2\left(x-y\right)}-\dfrac{x-y}{2\left(x+y\right)}+\dfrac{2y^2}{x^2-y^2}\)
d,\(\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
1.rút gọn biểu thuc P=\(\dfrac{2}{x+3}+\dfrac{1}{x-3}+\dfrac{9-x}{9-x^2}\) với x\(\ne-3vàx\ne3\)
2.thực hiện phép tính \(\left(2x^4-3x^3-3x^2+6x-1\right):\left(x^2-2\right)\)
\(\left(15x^4y^6-12^3y^4-18x^2y^3\right):\left(-6x^2y^2\right)\)