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a) \(\dfrac{36\left(x-2\right)^3}{32-16x}=\dfrac{36\left(x-2\right)^3}{16\left(2-x\right)}=\dfrac{36\left(x-2\right)^3}{-16\left(x-2\right)}\)\(=\dfrac{36\left(x-2\right)^3:4\left(x-2\right)}{-16\left(x-2\right):4\left(x-2\right)}\)\(=\dfrac{9\left(x-2\right)^2}{-4}\)
b) \(\dfrac{x^2-xy}{5y^2-5xy}=\dfrac{x\left(x-y\right)}{5y\left(y-x\right)}=\dfrac{x\left(x-y\right)}{-5y\left(x-y\right)}\)\(=\dfrac{x}{-5y}\)
Cho biểu thức
A= (\( {1 \over x-2}\)+\({1 \over x+2}\)) : \( {5-x \over x-2}\)
a) Tìm ĐKXĐ
b) Rút gọn A
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Bài 2
\(a,x^3+2x^2+x\)
\(=x.\left(x^2+2x+1\right)\)
\(b,xy+y^2-x-y\)
\(=y.\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right).\left(x+y\right)\)
bài 3
\(a,3x.\left(x^2-4\right)=0\)
\(\Rightarrow\orbr{\begin{cases}3x=0\\x^2=4\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x=2,x=-2\end{cases}}\)
vậy x=0,x=2 hay x=-2
\(b,xy+y^2-x-y=0\)
\(y.\left(x+y\right)-\left(x+y\right)=0\)
\(\left(y-1\right).\left(x+y\right)=0\)
\(\Rightarrow\orbr{\begin{cases}y-1=0\\x+y=0\end{cases}\Rightarrow\orbr{\begin{cases}y=1\\x=-1\end{cases}}}\)
vậy x=-1, y=1
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\(\frac{\left(-x\right).5.a^2}{x^2.\left(-a\right)^3}=\frac{5}{ã}\)
\(\frac{\left(-x\right)\cdot5\cdot a^2}{x^2\cdot\left(-a\right)^3}=\frac{\left(-x\right)\cdot5\cdot a^2}{\left(-x\right)\cdot\left(-x\right)\cdot a^2\cdot\left(-a\right)}=\frac{5}{ax}\)
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a) ta có : \(M=\frac{x+2}{x+3}-\frac{5}{x^2+x-6}+\frac{1}{2-x}\)\(=\frac{x+2}{x+3}+\frac{5}{\left(x+3\right)\left(2-x\right)}+\frac{1}{2-x}\)
\(=\frac{\left(x+2\right)\left(2-x\right)}{\left(x+3\right)\left(2-x\right)}+\frac{5}{\left(x+3\right)\left(2-x\right)}+\frac{1\left(x+3\right)}{\left(x+3\right)\left(2-x\right)}\)
\(=\frac{-x^2+4+5+x+3}{\left(x+3\right)\left(2-x\right)}\) \(=\frac{-x^2+x+12}{\left(x+3\right)\left(2-x\right)}\)
\(=\frac{\left(4-x\right)\left(x+3\right)}{\left(x+3\right)\left(2-x\right)}\) = \(\frac{4-x}{2-x}\)