cộng trừ các phân thức
\(x+\frac{1-2x}{9}+\frac{3x-2}{12}\)
K
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BC
1
20 tháng 11 2018
\(\frac{2x^2-11x}{2xy}+\frac{5y-x}{y}+\frac{x+2y}{x}\)
\(=\frac{2x^2-11x+\left(5y-x\right)2x+\left(x+2y\right)2y}{2xy}\)
\(=\frac{2x^2-11x+10xy-2x^2+2xy+4y^2}{2xy}=\frac{12xy-11x+4y^2}{2xy}\)
K
20 tháng 11 2018
\(x+y+\frac{3x^2}{2y}\)
\(=\frac{2xy}{2y}+\frac{2y^2}{2y}+\frac{3x^2}{2y}=\frac{2xy+2y^2+3x^2}{2y}=\frac{2y.\left(2x+y\right)+3x^2}{2y}=\frac{2x+y+3x^2}{2y}\)
p/s: mới lớp 7 ạ sai sót bỏ qua nha :>
BC
1
27 tháng 11 2018
ĐK: \(x\ne1\)
\(\frac{4x^2-3x+5}{\left(x-1\right)\left(x^2+x+1\right)}-\frac{1-2x}{x^2+x+1}-\frac{6}{x-1}\)
\(=\frac{4x^2-3x+5-\left(1-2x\right)\left(x-1\right)-6\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\frac{4x^2-3x+5+2x^2-3x+1-6x^2-6x-6}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(=\frac{-12x}{\left(x-1\right)\left(x^2+x+1\right)}\)
BC
2
27 tháng 11 2018
ĐKXĐ : \(x\ne-1\)
\(\frac{1}{2x+2}-\frac{x-1}{3x^2+6x+3}\)
\(=\frac{1}{2\left(x+1\right)}-\frac{x-1}{3\left(x^2+2x+1\right)}\)
\(=\frac{1}{2\left(x+1\right)}-\frac{x-1}{3\left(x+1\right)^2}\)
\(=\frac{3\left(x+1\right)}{2\left(x+1\right)\cdot3\left(x+1\right)}-\frac{2\left(x-1\right)}{3\left(x+1\right)^2\cdot2}\)
\(=\frac{3x+3}{6\left(x+1\right)^2}-\frac{2x-2}{6\left(x+1\right)^2}\)
\(=\frac{3x+3-2x+2}{6\left(x+1\right)^2}\)
\(=\frac{x+5}{6\left(x+1\right)^2}\)
20 tháng 11 2018
\(\frac{2x+y}{2x^2-xy}+\frac{8y}{y^2-4x^2}+\frac{2x-y}{2x^2+xy}\)
\(=\frac{2x+y}{x\left(2x-y\right)}-\frac{8y}{\left(2x-y\right)\left(2x+y\right)}+\frac{2x-y}{x\left(2x+y\right)}\)
\(=\frac{\left(2x+y\right)^2-8xy+\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}=\frac{4x^2+4xy+y^2-8xy+4x^2-4xy+y^2}{x\left(2x-y\right)\left(2x+y\right)}\)
\(=\frac{8x^2-8xy+2y^2}{x\left(2x-y\right)\left(2x+y\right)}=\frac{2\left(4x^2-4xy+y^2\right)}{x\left(2x-y\right)\left(2x+y\right)}\)
\(=\frac{2\left(2x-y\right)^2}{x\left(2x-y\right)\left(2x+y\right)}=\frac{2\left(2x-y\right)}{x\left(2x+y\right)}\)
TN
8 tháng 8 2018
\(\frac{1}{3x-2}-\frac{1}{3x+2}-\frac{3x-6}{4-9x^2}\)
\(=\frac{3x+2}{9x^2-4}-\frac{3x-2}{9x^2-4}+\frac{3x-6}{9x^2-4}\)
\(=\frac{3x+2-3x+2+3x-6}{9x^2-4}\)
\(=\frac{3x-2}{9x^2-4}\)
\(=\frac{1}{3x+2}\)
\(\frac{18}{\left(x-3\right)\left(x^2-9\right)}-\frac{3}{x^2-6x+9}-\frac{x^2}{x^2-9}\)
\(=\frac{18}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\) \(-\frac{3\left(x+3\right)}{\left(x-3\right)\left(x-3\right)\left(x+3\right)}\)\(-\frac{x^2\left(x-3\right)}{\left(x-3\right)\left(x+3\right)\left(x-3\right)}\)
\(=\frac{18-3x-9-x^3+3x^2}{\left(x-3\right)^2\left(x+3\right)}\)
\(=\frac{-x^3+3x^2-3x+9}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{\left(-x^2-3\right)\left(x-3\right)}{\left(x-3^2\right)\left(x+3\right)}\)
\(=\frac{-x^2-3}{\left(x-3\right)\left(x+3\right)}\)
học tốt
Ta có: MTC=36
Quy đồng
\(x=\frac{x.36}{36}\)
\(\frac{1-2x}{9}=\frac{\left(1-2x\right).4}{36}\)
\(\frac{3x-2}{12}=\frac{\left(3x-2\right).3}{36}\)
Ta có
:\(\frac{36x+4-8x+9x-6}{36}=\frac{37x-2}{36}\)