Thực hiện phép tính:
4x.(3x^2-4xy+5y^2)
\(\frac{4}{x-1}\) - \(\frac{2}{1-x}\) - \(\frac{x}{x-1}\)
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a) \(\frac{6xy+4y}{4x^2y^2}+\frac{2xy-4y}{4x^2y^2}\)
\(=\frac{6xy+4y+2xy-4y}{4x^2y^2}\)
\(=\frac{8xy}{4x^2y^2}\)
\(=\frac{2}{xy}\)
b) \(\frac{5}{x+3}-\frac{3}{x-3}+\frac{30}{x^2-9}\)
\(=\frac{5\left(x-3\right)}{\left(x+3\right)\left(x-3\right)}-\frac{3\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}+\frac{30}{\left(x-3\right)\left(x+3\right)}\)
\(=\frac{5x-15-3x-9+30}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2x+6}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2\left(x+3\right)}{\left(x+3\right)\left(x-3\right)}\)
\(=\frac{2}{x-3}\)
c) \(\frac{2x+8}{\left(x+2\right)^2}:\frac{x+4}{x+2}\)
\(=\frac{2\left(x+4\right)}{\left(x+2\right)^2}\cdot\frac{x+2}{x+4}\)
\(=\frac{2\left(x+4\right)\left(x+2\right)}{\left(x+2\right)\left(x+2\right)\left(x+4\right)}\)
\(=\frac{2}{x+2}\)
ĐKXĐ: \(x\ne2\)
\(\frac{3x-6}{x-2}\)
\(=\frac{3.\left(x-2\right)}{x-2}\)
\(=3\)
\(\left(x-1\right)\left(x-4\right)\left(x-5\right)\left(x-8\right)+36=0\)
\(\left[\left(x-1\right)\left(x-8\right)\right]\left[\left(x-4\right)\left(x-5\right)\right]+36=0\)
\(\left(x^2-9x+8\right)\left(x^2-9x+20\right)+36=0\)
Đặt \(a=x^2-9x+14\)ta có :
\(\left(a-6\right)\left(a+6\right)+36=0\)
\(a^2-6^2+36=0\)
\(a^2=0\)
Thay \(a=x^2-9x+14\)ta có :
\(\left(x^2-9x+14\right)^2=0\)
\(\Leftrightarrow x^2-9x+14=0\)
\(\Leftrightarrow x^2-2x-7x+14=0\)
\(\Leftrightarrow x\left(x-2\right)-7\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-7\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-2=0\\x-7=0\end{cases}\Rightarrow\orbr{\begin{cases}x=2\\x=7\end{cases}}}\)
Vậy,...........
\(\frac{4}{x-1}-\frac{2}{1-x}-\frac{x}{x-1}\)
\(=\frac{4}{x-1}+\frac{-2}{x-1}-\frac{x}{x-1}\)
\(=\frac{2-x}{x-1}\)
ĐKXĐ: \(x\ne1\)
\(\frac{4}{x-1}-\frac{2}{1-x}-\frac{x}{x-1}\)
\(=\frac{4}{x-1}+\frac{2}{x-1}-\frac{x}{x-1}\)
\(=\frac{4+2-x}{x-1}\)
\(=\frac{6-x}{x-1}\)