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a,
\(\Leftrightarrow A=\left(\frac{x+1}{\left(x+1\right)\left(x-1\right)}+\frac{x}{\left(x+1\right)\left(x-1\right)}\right):\frac{2x+1}{\left(x+1\right)^2}\)
\(\Leftrightarrow A=\frac{2x+1}{\left(x+1\right)\left(x-1\right)}\cdot\frac{\left(x+1\right)^2}{2x+1}\)
\(\Leftrightarrow A=\frac{x+1}{x-1}\)
b, dùng máy tính kq là-3
2x+1x2−2x+1 −2x+3x−1 =0
\(\frac{\left(2x+1\right)\left(x+1\right)}{\left(x-1\right)^2\left(x+1\right)}-\frac{\left(2x+3\right)\left(x-1\right)}{\left(x-1\right)^2\left(x+1\right)}=0.\)
\(\frac{2x^2+3x+1}{\left(x-1\right)^2\left(x+1\right)}-\frac{2x^2-x+3}{\left(x-1\right)^2\left(x+1\right)}=0\)
\(\frac{2x+4}{\left(x-1\right)^2\left(x+1\right)}=0\)
=> 2x+4=0
2x=-4
x=-2
Học tốt nhé!
6) Ta có
\(A=\frac{x^3}{y+2z}+\frac{y^3}{z+2x}+\frac{z^3}{x+2y}\)
\(=\frac{x^4}{xy+2xz}+\frac{y^4}{yz+2xy}+\frac{z^4}{zx+2yz}\)
\(\ge\frac{\left(x^2+y^2+z^2\right)^2}{xy+2xz+yz+2xy+zx+2yz}\)
\(\Leftrightarrow A\ge\frac{1}{3\left(xy+yz+zx\right)}\ge\frac{1}{3\left(x^2+y^2+z^2\right)}=\frac{1}{3}\)
A)\(ĐKXĐ:x\ne1;2;3;4;5\)
B)Ta có:\(P=\frac{1}{x^2-x}+\frac{1}{x^2-3x+2}+\frac{1}{x^2-5x+6}+\frac{1}{x^2-7x+12}+\frac{1}{x^2-9x+20}\)
\(=\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x^2-x\right)-\left(2x-2\right)}+\frac{1}{\left(x^2-2x\right)-\left(3x-6\right)}+\frac{1}{\left(x^2-3x\right)-\left(4x-12\right)}+\frac{1}{\left(x^2-4x\right)-\left(5x-20\right)}\)
\(=\frac{1}{x\left(x-1\right)}+\frac{1}{x\left(x-1\right)-2\left(x-1\right)}+\frac{1}{x\left(x-2\right)-3\left(x-2\right)}+\frac{1}{x\left(x-3\right)-4\left(x-3\right)}+\frac{1}{x\left(x-4\right)-5\left(x-4\right)}\)
\(=\frac{1}{x\left(x-1\right)}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-2\right)\left(x-3\right)}+\frac{1}{\left(x-3\right)\left(x-4\right)}+\frac{1}{\left(x-4\right)\left(x-5\right)}\)
\(=\frac{1}{x}-\frac{1}{x-1}+\frac{1}{x-1}-\frac{1}{x-2}+\frac{1}{x-2}-\frac{1}{x-3}+\frac{1}{x-3}-\frac{1}{x-4}+\frac{1}{x-4}-\frac{1}{x-5}=\frac{1}{x}-\frac{1}{x-5}=\frac{-5}{x\left(x-5\right)}\)
nhầm
\(\frac{1}{\left(x-1\right)x}+\frac{1}{\left(x-1\right)\left(x-2\right)}+\frac{1}{\left(x-3\right)\left(x-2\right)}+\frac{1}{\left(x-4\right)\left(x-3\right)}+\frac{1}{\left(x-5\right)\left(x-4\right)}\)
\(=\frac{1}{x-1}-\frac{1}{x}+\frac{1}{x-2}-\frac{1}{x-1}+\frac{1}{x-3}-\frac{1}{x-2}+\frac{1}{x-4}-\frac{1}{x-3}+\frac{1}{x-5}-\frac{1}{x-4}=\frac{1}{x-5}-\frac{1}{x}=\frac{5}{\left(x-5\right)x}\)
Xin lỗi nha
\(\frac{a}{x+1}+\frac{b}{1-x}\)
\(=\frac{a\left(1-x\right)+b\left(x+1\right)}{\left(x+1\right)\left(1-x\right)}\)
\(=\frac{a-a.x+bx+b}{1-x^2}\)
\(=\frac{\left(b-a\right).x+\left(a+b\right)}{1-x^2}=\frac{1}{1-x^2}\)
\(\Leftrightarrow\left(b-a\right)x+\left(a+b\right)=1\)
Sử dụng đồng nhất hệ số :
\(\hept{\begin{cases}b-a=0\\a+b=1\end{cases}}\)
\(\Rightarrow a=b=\frac{1}{2}\)
Vậy ...
X=1
tính máy tính là ra mà
\(\frac{1+x^2+\frac{1}{x+1}}{2+\frac{1}{x+1}}=1\) sau đó nhấn shift+solve sau đó nhấn bất kì số nào đấy tiếp là nhấn =