Ôn tập: Phân thức đại số
Các câu hỏi tương tự
giải phương trình
1)\(\left(x-2\right)\left(3+2x\right)-2x\left(x+5\right)=6\)
2)\(x^2-4-\left(x-5\right)\left(x-2\right)=0\)
3)\(\dfrac{x-3}{3}-\dfrac{x+2}{2}=\dfrac{x}{6}\)
4)\(\dfrac{x+2}{x-2}-\dfrac{x-2}{x+2}+\dfrac{3x-1}{x-4}-6\)
5)\(\dfrac{96}{x^2-16}=\dfrac{2x-1}{x+4}+\dfrac{3x-1}{x-4}-6\)
Thực hiện các phép tính :
a) left(dfrac{9}{x^3-9x}+dfrac{1}{x+3}right):left(dfrac{x-3}{x^2+3x}-dfrac{x}{3x+9}right)
b) left(dfrac{2}{x-2}-dfrac{2}{x+2}right).dfrac{x^2+4x+4}{8}
c) left(dfrac{3x}{1-3x}+dfrac{2x}{3x+1}right):dfrac{6x^2+10x}{1-6x+9x^2}
d) left(dfrac{x}{x^2-25}-dfrac{x-5}{x^2+5x}right):dfrac{2x-5}{x^2+5x}+dfrac{x}{5-x}
e) left(dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+dfrac{y}{x^2+y^2}right):left(dfrac{1}{x-y}-dfrac{2xy}{x^3-x^2y+xy^2-y^3}right)
Đọc tiếp
Thực hiện các phép tính :
a) \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
b) \(\left(\dfrac{2}{x-2}-\dfrac{2}{x+2}\right).\dfrac{x^2+4x+4}{8}\)
c) \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
d) \(\left(\dfrac{x}{x^2-25}-\dfrac{x-5}{x^2+5x}\right):\dfrac{2x-5}{x^2+5x}+\dfrac{x}{5-x}\)
e) \(\left(\dfrac{x^2+xy}{x^3+x^2y+xy^2+y^3}+\dfrac{y}{x^2+y^2}\right):\left(\dfrac{1}{x-y}-\dfrac{2xy}{x^3-x^2y+xy^2-y^3}\right)\)
Bài 1: Rút gon
a) B=\(\left(\dfrac{x}{3x-9}+\dfrac{2x-3}{3x-x^2}\right).\dfrac{3x^2-9x}{x^2+6x+9}\)
b) A=\(\left(\dfrac{x}{x^2-4}+\dfrac{2}{2-x}+\dfrac{1}{x+2}\right):\dfrac{1}{x+2}\)
a,\(\dfrac{x+1}{x-3}+\dfrac{-2x^2+2x}{x^2-9}+\dfrac{x-1}{x+3}\)
b,\(\dfrac{1-2x}{6x^3y}+\dfrac{3+2y}{6x^3y}+\dfrac{2x-4}{6x^3y}\)
c,\(\dfrac{5}{2x^2y}+\dfrac{3}{5xy^2}+\dfrac{x}{3y^3}\)
d,\(\dfrac{5}{4\left(x+2\right)}+\dfrac{8-x}{4x^2+8x}\)
c,\(\dfrac{x^2+2}{x^3+1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
rút gọn các biểu thức sau :
a, \(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{9x^2-6x+1}\)
b, \(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
c, \(\dfrac{1-x^2}{x}\left(\dfrac{x^2}{x+3}-1\right)+\dfrac{3x^2-14x+3x}{x^2+3x}\)
Mí bác ơi~~Ai giải giúp em với~Em đang cần gấp lắm a~~Em cảm ơn các bác nhiều nhiều lắm a
bài 1:
b,left(dfrac{3x}{1-3x}+dfrac{2x}{3x+1}right):dfrac{6x^2+10x}{1-6x+9x^2}
c,
dfrac{x-1}{x^3}-dfrac{x+1}{x^3-x^2}+dfrac{3}{x^3-2x^2+x}
d,left(dfrac{9}{x^3-9x}+dfrac{1}{x+3}right):left(dfrac{x-3}{x^2+3x}-dfrac{x}{3x+9}right)
e,dfrac{x+1}{x+2}:left(dfrac{x+2}{x+3}:dfrac{x+3}{x+1}right)
Bài 2:Rút gọn
a,dfrac{dfrac{1}{x}+dfrac{1}{y}}{dfrac{1}{x}-dfrac{1}{y}}
b,
dfrac{dfrac{x}{x+1}-dfrac{x-1}{x}}...
Đọc tiếp
Mí bác ơi~~Ai giải giúp em với~Em đang cần gấp lắm a~~Em cảm ơn các bác nhiều nhiều lắm a
bài 1:
b,\(\left(\dfrac{3x}{1-3x}+\dfrac{2x}{3x+1}\right):\dfrac{6x^2+10x}{1-6x+9x^2}\)
c,
\(\dfrac{x-1}{x^3}-\dfrac{x+1}{x^3-x^2}+\dfrac{3}{x^3-2x^2+x}\)
d,\(\left(\dfrac{9}{x^3-9x}+\dfrac{1}{x+3}\right):\left(\dfrac{x-3}{x^2+3x}-\dfrac{x}{3x+9}\right)\)
e,\(\dfrac{x+1}{x+2}:\left(\dfrac{x+2}{x+3}:\dfrac{x+3}{x+1}\right)\)
Bài 2:Rút gọn
a,\(\dfrac{\dfrac{1}{x}+\dfrac{1}{y}}{\dfrac{1}{x}-\dfrac{1}{y}}\)
b,
\(\dfrac{\dfrac{x}{x+1}-\dfrac{x-1}{x}}{\dfrac{x}{x-1}-\dfrac{x+1}{x}}\)
c,\(1-\dfrac{x}{1-\dfrac{x}{x+1}}\)
d,\(\dfrac{1-\dfrac{2}{x+1}}{1-\dfrac{x^2-2}{x^2-1}}\)
Chứng minh đẳng thức :
a) left(dfrac{x^2-2x}{2x^2+8}-dfrac{2x^2}{8-4x+2x^2-x^3}right)left(1-dfrac{1}{x}-dfrac{2}{x^2}right)dfrac{x+1}{2x}
b) left[dfrac{2}{3x}-dfrac{2}{x+1}left(dfrac{x+1}{3}-x-1right)right]:dfrac{x-1}{x}dfrac{2x}{x-1}
c) left[dfrac{2}{left(x+1right)^3}.left(dfrac{1}{x}+1right)+dfrac{1}{x^2+2x+1}left(dfrac{1}{x^2}+1right)right]:dfrac{x-1}{x^3}dfrac{x}{x-1}
Đọc tiếp
Chứng minh đẳng thức :
a) \(\left(\dfrac{x^2-2x}{2x^2+8}-\dfrac{2x^2}{8-4x+2x^2-x^3}\right)\left(1-\dfrac{1}{x}-\dfrac{2}{x^2}\right)=\dfrac{x+1}{2x}\)
b) \(\left[\dfrac{2}{3x}-\dfrac{2}{x+1}\left(\dfrac{x+1}{3}-x-1\right)\right]:\dfrac{x-1}{x}=\dfrac{2x}{x-1}\)
c) \(\left[\dfrac{2}{\left(x+1\right)^3}.\left(\dfrac{1}{x}+1\right)+\dfrac{1}{x^2+2x+1}\left(\dfrac{1}{x^2}+1\right)\right]:\dfrac{x-1}{x^3}=\dfrac{x}{x-1}\)
bài tập 1: giải các phương trình sau:
a, dfrac{3}{1-4x} dfrac{2}{4x+1}- dfrac{8+6x}{16x^2-1}
b, dfrac{3}{5x-1}+dfrac{2}{3-5x}dfrac{4}{left(1-5xright)left(5x-3right)}
c, dfrac{x+2}{x+1}+dfrac{3}{x-2}dfrac{3}{x^2-x-2}+1
d, dfrac{5-x}{4x^2-8x}+dfrac{7}{8}dfrac{x-1}{2xleft(x-2right)}+dfrac{1}{8x-16}
e, dfrac{x+6}{x+5}+dfrac{x-5}{x+6}dfrac{2x^2+23x+61}{x^2+x-30}
f, dfrac{x^2-x}{x+3}-dfrac{x^2}{x-3}dfrac{7x^2-3x}{9-x^2}
Đọc tiếp
bài tập 1: giải các phương trình sau:
a, \(\dfrac{3}{1-4x}\)= \(\dfrac{2}{4x+1}\)- \(\dfrac{8+6x}{16x^2-1}\)
b, \(\dfrac{3}{5x-1}\)+\(\dfrac{2}{3-5x}\)=\(\dfrac{4}{\left(1-5x\right)\left(5x-3\right)}\)
c, \(\dfrac{x+2}{x+1}\)+\(\dfrac{3}{x-2}\)=\(\dfrac{3}{x^2-x-2}+1\)
d, \(\dfrac{5-x}{4x^2-8x}+\dfrac{7}{8}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8x-16}\)
e, \(\dfrac{x+6}{x+5}+\dfrac{x-5}{x+6}=\dfrac{2x^2+23x+61}{x^2+x-30}\)
f, \(\dfrac{x^2-x}{x+3}-\dfrac{x^2}{x-3}=\dfrac{7x^2-3x}{9-x^2}\)
quy đồng các phân thức sau
a,\(\dfrac{x+1}{x-1};\dfrac{x-1}{x+1};\dfrac{4}{1-x^2}\)
b,\(\dfrac{x^3}{x^3-3x^2y+3xy^2-y^3};\dfrac{x}{y^2xy}\)
c,\(\dfrac{4x}{x-2};\dfrac{3x}{x-2};\dfrac{12x}{x^2-4}\)
d,\(\dfrac{7}{x};\dfrac{x}{x+6};\dfrac{36}{x^2+6x}\)