Rút gọn phân thức \(\dfrac{x^2+4y^2-4xy-4}{2x^2-4xy+4x}\) \(\dfrac{x-2y-2}{2x}\) \(\dfrac{x+2y+2}{2x}\) \(\dfrac{x+y}{2x}\) \(\dfrac{x-y}{2x}\) Hướng dẫn giải: \(\dfrac{x^2+4y^2-4xy-4}{2x^2-4xy+4x}\) \(=\dfrac{\left(x-2y\right)^2-2^2}{2x\left(x-2y+2\right)}\) \(=\dfrac{\left(x-2y-2\right)\left(x-2y+2\right)}{2x\left(x-2y+2\right)}\) \(=\dfrac{x-2y-2}{2x}\)
Thực hiện phép tính \(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}\) \(\dfrac{x-y}{xy}\) \(\dfrac{x^2-xy+y^2}{xy\left(x-y\right)}\) \(\dfrac{x+y}{xy}\) \(\dfrac{x^2+2xy+y^2}{xy\left(x-y\right)}\) Hướng dẫn giải: \(\dfrac{x}{xy-y^2}+\dfrac{2x-y}{xy-x^2}\) \(=\dfrac{x}{y\left(x-y\right)}+\dfrac{2x-y}{x\left(y-x\right)}\) \(=\dfrac{x}{y\left(x-y\right)}-\dfrac{2x-y}{x\left(x-y\right)}\) \(=\dfrac{x^2-y\left(2x-y\right)}{xy\left(x-y\right)}\) \(=\dfrac{x^2-2xy+y^2}{xy\left(x-y\right)}\) \(=\dfrac{\left(x-y\right)^2}{xy\left(x-y\right)}\) \(=\dfrac{x-y}{xy}\)
Rút gọn biểu thức \(\dfrac{4a^2-3a+5}{a^3-1}-\dfrac{1-2a}{a^2+a+1}-\dfrac{6}{a-1}\) \(\dfrac{-9a}{a^3-1}\) \(\dfrac{9a}{a^3-1}\) \(\dfrac{9}{a^2+a+1}\) \(\dfrac{9a}{a^2+a+1}\) Hướng dẫn giải: \(\dfrac{4a^2-3a+5}{a^3-1}-\dfrac{1-2a}{a^2+a+1}-\dfrac{6}{a-1}\) \(=\dfrac{4a^2-3a+5-\left(1-2a\right)\left(a-1\right)-6\left(a^2+a+1\right)}{\left(a-1\right)\left(a^2+a+1\right)}\) \(=\dfrac{4a^2-3a+5-\left(-2a^2+3a-1\right)-6a^2-6a-6}{\left(a-1\right)\left(a^2+a+1\right)}\) \(=\dfrac{4a^2-3a+5+2a^2-3a+1-6a^2-6a-6}{\left(a-1\right)\left(a^2+a+1\right)}\) \(=\dfrac{-9a}{a^3-1}\)
Cho biểu thức \(P=\dfrac{3x^2+3x}{\left(x+1\right)\left(2x-6\right)}\). Tìm giá trị của x để \(P=1\). \(x=-6\) \(x=3\) \(x=7\) \(x=-10\) Hướng dẫn giải: Điều kiện xác định: \(x\ne-1;x\ne3\) \(P=\dfrac{3x^2+3x}{\left(x+1\right)\left(2x-6\right)}\)\(=\dfrac{3x\left(x+1\right)}{2\left(x+1\right)\left(x-3\right)}=\dfrac{3x}{2\left(x-3\right)}\). Để \(P=1\) thì \(\dfrac{3x}{2\left(x-3\right)}=1\)\(\Leftrightarrow3x=2\left(x-3\right)\)\(\Leftrightarrow x=-6\) (Tmđk).
Rút gọn biểu thức \(P=\dfrac{x+2}{x+3}-\dfrac{5}{x^2+x-6}+\dfrac{1}{2-x}\) \(\dfrac{x-4}{x-2}\) \(\dfrac{x+4}{x-2}\) \(-\dfrac{x-4}{x-2}\) \(-\dfrac{x+4}{x-2}\) Hướng dẫn giải: \(P=\dfrac{x+2}{x+3}-\dfrac{5}{x^2+x-6}+\dfrac{1}{2-x}\) \(=\dfrac{x+2}{x+3}-\dfrac{5}{\left(x+3\right)\left(x-2\right)}-\dfrac{1}{x-2}\) \(=\dfrac{\left(x+2\right)\left(x-2\right)-5-\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\) \(=\dfrac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\) \(=\dfrac{\left(x+3\right)\left(x-4\right)}{\left(x+3\right)\left(x-2\right)}\) \(=\dfrac{x-4}{x-2}\).
Cho biểu thức \(P=\dfrac{x+2}{x+3}-\dfrac{5}{x^2+x-6}+\dfrac{1}{2-x}\). Tìm x để \(P=\dfrac{1}{5}\) \(x=\dfrac{9}{2}\) \(x=4\) \(x=\dfrac{7}{2}\) \(x=\dfrac{5}{2}\) Hướng dẫn giải: \(P=\dfrac{x+2}{x+3}-\dfrac{5}{x^2+x-6}+\dfrac{1}{2-x}\) \(=\dfrac{x+2}{x+3}-\dfrac{5}{\left(x+3\right)\left(x-2\right)}-\dfrac{1}{x-2}\) \(=\dfrac{\left(x+2\right)\left(x-2\right)-5-\left(x+3\right)}{\left(x+3\right)\left(x-2\right)}\) \(=\dfrac{x^2-x-12}{\left(x+3\right)\left(x-2\right)}\) \(=\dfrac{\left(x+3\right)\left(x-4\right)}{\left(x+3\right)\left(x-2\right)}\) \(=\dfrac{x-4}{x-2}\). Để \(P=\dfrac{1}{5}\) thì \(\dfrac{x-4}{x-2}=\dfrac{1}{5}\Leftrightarrow5\left(x-4\right)=x-2\)\(\Leftrightarrow4x=18\)\(\Leftrightarrow x=\dfrac{9}{2}\)
