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a,\(A=\frac{6x+12}{\left(x+2\right)\left(2x-6\right)}=\frac{6\left(x+2\right)}{2\left(x+2\right)\left(x-3\right)}=\frac{3}{x-3}\)
b, Giá trị của x để phân thức có giá trị bằng (-2) :
\(\frac{3}{x-3}=-2\Rightarrow x=1,5\)
\(B=\left(\frac{2x}{x-3}-\frac{x-1}{x+3}+\frac{x^2+1}{9-x^2}\right):\left(1-\frac{x-1}{x+3}\right)\left(ĐK:x\ne\pm3\right)\)
\(=\frac{2x\left(x+3\right)-\left(x-1\right)\left(x-3\right)-x^2-1}{x^2-9}:\frac{x+3-x+1}{x+3}\)
\(=\frac{2x^2+6x-x^2+3x+x-3-x^2-1}{\left(x-3\right)\left(x+3\right)}\cdot\frac{x+3}{4}\)
\(=\frac{10x-4}{\left(x-3\right)\left(x+3\right)}\cdot\frac{x+3}{4}=\frac{10x-4}{4\left(x-3\right)}\)
\(B=\left(\frac{2x}{x-3}-\frac{x+1}{x+3}+\frac{x^2+1}{9-x^2}\right):\left(1-\frac{x-1}{x+3}\right)\)
\(=\left[\frac{2x\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{\left(x+1\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}-\frac{x^2+1}{\left(x-3\right)\left(x+3\right)}\right]:\left(\frac{x+3-x+1}{x+3}\right)\)
\(=\left(\frac{2x^2+6x-x^2+3x-x+3-x^2-1}{\left(x+3\right)\left(x-3\right)}\right):\frac{4}{x+3}\)
\(=\frac{8x-1}{\left(x+3\right)\left(x-3\right)}.\frac{x+3}{4}\)\(=\frac{8x-1}{4\left(x-3\right)}\)
a/ \(\frac{7x-14y}{x^2-4y^2}=\frac{7\left(x-2y\right)}{x^2-\left(2y\right)^2}=\frac{7\left(x-2y\right)}{\left(x-2y\right)\left(x+2y\right)}=\frac{7}{x+2y}.\)
b/ \(\frac{1-\frac{2y}{x}+\frac{y^2}{x^2}}{\frac{1}{x}-\frac{1}{y}}=\frac{\frac{x^2-2xy+y^2}{x^2}}{\frac{y-x}{xy}}=\frac{\left(x-y\right)^2}{x^2}.\frac{xy}{-\left(x-y\right)}=-\frac{y\left(x-y\right)}{x}=\frac{y\left(y-x\right)}{x}\)
\(\left(\frac{x}{x-1}-\frac{x+1}{x}\right):\left(\frac{x}{x+1}-\frac{x-1}{x}\right)\)
\(=\left(\frac{x^2-\left(x-1\right)\left(x+1\right)}{\left(x-1\right).x}\right):\left(\frac{x^2-\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}\right)\)
\(=\frac{x^2-\left(x-1\right)\left(x+1\right)}{x\left(x-1\right)}.\frac{x\left(x+1\right)}{x^2-\left(x-1\right)\left(x+1\right)}\)
\(=\frac{x+1}{x-1}\)