Cộng các phân thức: 1 x - y y - z + 1 y - z z - x + 1 z - x x - y
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Làm phếp tính cộng các phân thức sau 2x-3y/xy-y²+1/x-y
\(=\dfrac{2x-3y}{y\left(x-y\right)}+\dfrac{1}{x-y}=\dfrac{2x-3y+y}{y\left(x-y\right)}=\dfrac{2x-2y}{y\left(x-y\right)}=\dfrac{2}{y}\)
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\(\dfrac{2x-3y}{xy-y^2}+\dfrac{1}{x-y}=\dfrac{2x-3y}{y\left(x-y\right)}+\dfrac{1}{x-y}=\dfrac{2x-3y+y}{y\left(x-y\right)}=\dfrac{2x-2y}{y\left(x-y\right)}=\dfrac{2}{y}.\)
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*Cộng các phân thức sau:a) x^2/x+1 + 2x/x^2-1 + 1/1+x+1 b) 2x+y/2x^2-y + 8y/y^2-4x^2+2x-y/2x^2+xy
a) \(\dfrac{x^2}{x+1}+\dfrac{2x}{x^2-1}+\dfrac{1}{1+x+1}\) \(=\dfrac{x^2.\left(x-1\right)\left(x+2\right)}{\left(x+1\right).\left(x-1\right)\left(x+2\right)}+\dfrac{2x.\left(x+2\right)}{\left(x-1\right).\left(x+1\right).\left(x+2\right)}+\dfrac{\left(x-1\right).\left(x+1\right)}{\left(x-1\right)\left(x+1\right).\left(x+2\right)}\)
\(=\dfrac{x^2.\left(x-1\right).\left(x+2\right)+2x.\left(x+2\right)+\left(x-1\right)\left(x+1\right)}{\left(x+1\right).\left(x-1\right).\left(x+2\right)}\)
\(=\dfrac{x^4+x^3-2x^2+2x^2+4x+x^2-1}{\left(x-1\right)\left(x+1\right).\left(x+2\right)}\)
\(=\dfrac{x^4+x^3+x^2+4x-1}{\left(x^2-1\right).\left(x+2\right)}\)
\(=\dfrac{x^4+x^3+x^2+4x-1}{x^3+2x^2-x-2}\)
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Cộng các phân thức
a ) 1/( x-y)(y-z) + 1/ ( y-z)(z-x) + 1/ (z-x)(x-y) b ) 4/(y-x)(z-x) + 3/(y-x)(y-z)+ 3/(y-x)(x-z)
a ) \(\frac{1}{\left(x-y\right)\left(y-z\right)}+\frac{1}{\left(y-z\right)\left(z-x\right)}+\frac{1}{\left(z-x\right)\left(x-y\right)}\)
= \(\frac{z-x}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}+\frac{x-y}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}+\frac{y-z}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}\)
= \(\frac{z-x+x-y+y-z}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}=0\)
b ) \(\frac{4}{\left(y-x\right)\left(z-x\right)}+\frac{3}{\left(y-x\right)\left(y-z\right)}+\frac{3}{\left(y-z\right)\left(x-z\right)}\)
= \(\frac{-4}{\left(y-x\right)\left(x-z\right)}+\frac{3}{\left(y-x\right)\left(y-z\right)}+\frac{3}{\left(y-z\right)\left(x-z\right)}\)
= \(\frac{-4\left(y-z\right)}{\left(x-z\right)\left(y-z\right)\left(y-x\right)}+\frac{3\left(x-z\right)}{\left(x-z\right)\left(y-z\right)\left(y-x\right)}+\frac{3\left(y-x\right)}{\left(x-z\right)\left(y-z\right)\left(y-x\right)}\)
= \(\frac{-4y+4z+3x-3z+3y-3x}{\left(x-z\right)\left(y-z\right)\left(y-x\right)}=\frac{z-y}{\left(x-z\right)\left(y-z\right)\left(y-x\right)}\)
= \(\frac{-\left(y-x\right)}{\left(x-z\right)\left(y-z\right)\left(y-x\right)}=\frac{-1}{\left(x-z\right)\left(y-z\right)}=\frac{1}{\left(x-z\right)\left(x-y\right)}\)
Chúc bạn học tốt !!!
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cộng trừ các phân thức
\(\frac{1}{x-y}+\frac{3xy}{y^3-x^3}+\frac{x-y}{x^2+xy+y^2}\)
Cộng các phân thức:
a) x/xy-y^2 + 2x-y/xy-x^2
b) 1/x+1 + 1/x-1 + 2x^2/x^2-1
a, \(\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}=\frac{x}{y\left(x-y\right)}+\frac{2x-y}{x\left(y-x\right)}\)
\(=\frac{x^2}{xy\left(x-y\right)}-\frac{2xy-y^2}{xy\left(x-y\right)}=\frac{\left(x-y\right)^2}{xy\left(x-y\right)}=\frac{x-y}{xy}\)
b, \(\frac{1}{x+1}+\frac{1}{x-1}+\frac{2x^2}{x^2-1}=\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{x+1}{\left(x-1\right)\left(x+1\right)}+\frac{2x^2}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x-1+x+1+2x^2}{\left(x-1\right)\left(x+1\right)}=\frac{2x+2x^2}{\left(x-1\right)\left(x+1\right)}=\frac{2x\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}=\frac{2x}{x-1}\)
*Cộng các phân thức sau: a) x^2/x+1 + 2x/x^2-1 + 1/1+x+1 b) 2x+y/2x^2-y + 8y/y^2-4x^2+2x-y/2x^2+xy c) 1/x-y +3xy/y^3-x^3 + x-y/x^2+xy+y^2
*Cộng các phân thức sau:
a) x^2/x+1 + 2x/x^2-1 + 1/1+x+1
b) 2x+y/2x^2-y + 8y/y^2-4x^2+2x-y/2x^2+xy
c) 1/x-y +3xy/y^3-x^3 + x-y/x^2+xy+y^2
plz
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a, \(\frac{x^2}{x+1}+\frac{2x}{x^2-1}+\frac{1}{x+1}+1\)
\(=\frac{x^2\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}-\frac{2x}{\left(x-1\right)\left(x+1\right)}+\frac{x-1}{\left(x+1\right)\left(x-1\right)}+\frac{\left(x+1\right)\left(x-1\right)}{\left(x+1\right)\left(x-1\right)}\)
\(=\frac{x^3-x^2-2x+x-1-x^2-1}{\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x^3-2x^2-x-2}{\left(x-1\right)\left(x+1\right)}\)
Cộng các phân thức khác mẫu thức: x + 2 5 x 3 y + y - 3 6 x 2 y
Cộng các phân thức đại số :
\(\frac{1}{\left(x-y\right)\left(y-z\right)}+\frac{1}{\left(y-z\right)\left(z-x\right)}+\frac{1}{\left(z-x\right)\left(x-y\right)}\)
\(\frac{1}{\left(x-y\right)\left(y-z\right)}+\frac{1}{\left(y-z\right)\left(z-x\right)}+\frac{1}{\left(z-x\right)\left(x-y\right)}\)
\(=\frac{z-x+x-y+y-z}{\left(x-y\right)\left(y-z\right)\left(z-x\right)}\)
\(=0\)
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