Tính
a, \(\frac{1}{\left(y-1\right)\left(y-2\right)}+\frac{2}{\left(2-y\right)\left(3y-y\right)}+\frac{3}{\left(1-y\right)\left(y-3\right)}\)
b, \(\frac{x^2}{x+1}+\frac{2x}{x^2-1}-\frac{1}{1-x}+1\)
c, \(\frac{1}{x^2+3x+2}-\frac{2x}{x^2+4x^2+4x}+\frac{1}{x^2+5x+6}\)
\(a,\frac{3x^2-6xy+3y^2}{5x^2-5xy+5y^2}:\frac{10x-10y}{x^3+y^3}\)
\(b,(\frac{x+2}{x+1}-\frac{2x}{x-1}).\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)
\(c,\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)-\frac{x^2-y^2}{\left(x-y\right)^2}\)
\(d,\frac{\frac{x-y}{x+y}-\frac{x+y}{x-y}}{1-\frac{x^2}{x^2+y^2}}\)
\(e,\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right).\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}+\frac{2x-2}{x^2+2x}\)
\(A,\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}\right):\left(\frac{1}{x+1}-\frac{x}{1-x}+\frac{2}{x^2-1}\right)=\frac{4x}{\left(x+1\right)^2}\)
\(B,\frac{2+x}{2-x}:\frac{4x^2}{4-4x+x^2}\cdot\left(\frac{2}{2-x}-\frac{4}{8+x^2}\cdot\frac{4-2x+x^2}{2-x}\right)=\frac{1}{2x}\)
\(C,\left[\left(\frac{3}{x-y}+\frac{3x}{x^2-y^2}\right):\frac{2x+y}{x^2+2xy+y^2}\right]\cdot\frac{x-y}{3}=xy\)
Chứng minh đẳng thức ( tìm x)
mọi người giải dùm mình cảm ơn
2) Giải phương trình
a) \(\frac{x+1}{x-2}+\frac{x-1}{x+2}=\frac{2\left(x^2+2\right)}{x^2-4}\)
b) \(\left(2x+3\right).\left(\frac{3x+8}{2-7x}+1\right)=\left(x-5\right).\left(\frac{3x+8}{2-7x}+1\right)\)
3) Rút gọn
a) \(\frac{2x-1}{x^3+1}+\frac{2x}{x^2-x+1}+\frac{-x}{x+1}+2\)
b) \(\frac{x+1}{2x-2}+\frac{x^2+3}{2-2x^2}+\frac{1}{1-x}-1,5\)
c) \(\left(\frac{x^2}{x^3-4x}-\frac{6}{3x-6}+\frac{1}{x+2}\right).\frac{x+2}{6}\)
d) \(\left(\frac{x}{xy-y^2}+\frac{2x-y}{xy-x^2}\right):\frac{x^2-2xy+y^2}{x^2y-xy^2}\)
e) \([\frac{1}{\left(2x-y\right)^2}+\frac{2}{4x^2-y^2}-\frac{1}{\left(2x+y\right)^2}].\frac{x^2+4xy+y^2}{16x}\)
Mn giúp mik vs mik đang cần gấp
Chứng minh \(A,\frac{\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}\right)}{\left(\frac{1}{x+1}-\frac{x}{1-x}+\frac{2}{x^2-1}\right)}=\frac{4x}{\left(x+1\right)^2}\)
\(B,\frac{\frac{2+x}{2-x}}{\frac{4x^2}{4-4x+x^2}}\cdot\left(\frac{2}{2-x}-\frac{4}{8+x2}\cdot\frac{4-2x+x^2}{2-x}\right)=\frac{1}{2x}\)
\(C,\frac{\orbr{\left(\frac{3}{x-y}+\frac{3x}{x^2-y^2}\right)}}{\frac{2x+y}{x^2+2xy+y^2}đóngngocvuong}\cdot\frac{x-y}{3}=xy\)
xin lỗi mọi người cái phân số dài là dấu chia nhé tại mình không biết viết sao với cái đóng ngoặc vuông nữa nhé xin lỗi lần nữa ạ
\(B=\left[\left(\frac{x}{y}-\frac{y}{x}\right):\left(x-y\right)-2\left(\frac{1}{y}-\frac{1}{x}\right)\right]:\frac{x-y}{y}\)
\(C=\left(\frac{x+y}{2x-2y}-\frac{x-y}{2x+2y}-\frac{2y^2}{y-x}\right):\frac{2y}{x-y}\)
\(D=3x:\left\{\frac{x^2-y^2}{x^3+y^3}\left[\left(x-\frac{x^2+y^2}{y}\right):\left(\frac{1}{x}-\frac{1}{y}\right)\right]\right\}\)
\(E=\frac{2}{x\left(x+1\right)}+\frac{2}{\left(x+1\right)\left(x+2\right)}+\frac{2}{\left(x+2\right)\left(x+3\right)}\)
Rút gọn :
A=\(\left(\frac{x+1}{x-1}-\frac{x-1}{x+1}\right):\left(\frac{1}{x+1}-\frac{x}{1-x}+\frac{z}{x^2-1}\right)\)
B= \([\left(\frac{3}{x-y}+\frac{3x}{x^2-y^2}\right):\frac{2x+y}{x^2+2xy+y^2}].\frac{x-9}{3}\)
1.Tính:
\(x:\frac{x-1}{2}-\frac{\left(x-1\right)\left(x^2+4x+1\right)}{2x^2+2x}.\frac{-4x}{\left(x-1\right)^2}-\frac{4x^2}{x^2-1}\)
2.Chứng minh đẳng thức sau( giả sử đẳng thức có nghĩa):
\(\frac{y-z}{\left(x-y\right)\left(x-z\right)}+\frac{z-x}{\left(y-z\right)\left(y-x\right)}+\frac{x-y}{\left(z-x\right)\left(z-y\right)}=\frac{2}{x-y}+\frac{2}{y-z}+\frac{2}{z-x}\)
Các bạn giúp mình với!
bài 1: tính
\(A=\frac{4^2-3x+17}{x^3-1}+\frac{2x-1}{x^2+x+1}+\frac{6}{1-x}\)
\(B=\frac{3x+1}{x^2-2x+1}-\frac{1}{x+1}+\frac{x+3}{1-x^2}\)
\(C=\left(\frac{x}{x+1}+1\right):\left(1-\frac{3x^2}{1-x2}\right)\)
\(D=\left(\frac{x^2}{y^2}+\frac{y}{x}\right):\left(\frac{x}{y^2}-\frac{1}{y}+\frac{1}{x}\right)\)
\(E=\left(\frac{1}{x^2+4x+4}-\frac{1}{x^2-4x+4}\right):\left(\frac{1}{x+2}+\frac{1}{x-2}\right)\)
\(F=\frac{1}{x-1}-\frac{x^3-x}{x^2+1}\left(\frac{1}{x^2-2x+1}+\frac{1}{1-x^2}\right)\)
Mấy thánh ơi giúp em với mai phải nộp rồi!!!!!!!!!!!!!!!