Giải các phương trình,bất phương trình:
c,\(\frac{\left(x-2\right)^2}{3}-\frac{\left(2x-3\right)\left(2x+3\right)}{8}+\frac{\left(x-4\right)^2}{6}=0\)
d,\(\frac{4}{-25x^2+20x-3}=\frac{3}{5x-1}-\frac{2}{5x-3}\)
e,\(\frac{1}{x^2-3x+2}+\frac{1}{x^2-5x+6}-\frac{2}{x^2-4x+3}=0\)
g,\(\frac{x-1}{2x^2-4x}-\frac{7}{8x}=\frac{5-x}{4x^2-8x}-\frac{1}{8x-16}\)
h,\(\frac{1}{x^2+9x+20}+\frac{1}{x^2+11x+30}+\frac{1}{x^2+13x+42}=\frac{1}{18}\)
i,\(\left(2x-5\right)^2-\left(x+2\right)^2=0\)
k,\(\left(3x^2+10x-8\right)^2=\left(5x^2-2x+10\right)^2\)
l,\(\left(x^2-2x+1\right)-4=0\)
m,\(4x^2+4x++1=x^2\)
Xin đáy ai giúp mình đi
\(a,\frac{3x^2-6xy+3y^2}{5x^2-5xy+5y^2}:\frac{10x-10y}{x^3+y^3}\)
\(b,(\frac{x+2}{x+1}-\frac{2x}{x-1}).\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)
\(c,\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)-\frac{x^2-y^2}{\left(x-y\right)^2}\)
\(d,\frac{\frac{x-y}{x+y}-\frac{x+y}{x-y}}{1-\frac{x^2}{x^2+y^2}}\)
\(e,\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right).\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}+\frac{2x-2}{x^2+2x}\)
Giải các phương trình sau :
\(a,6x^2-5x+3=2x-3x\left(3-2x\right)\)
\(b,\frac{2\left(x-4\right)}{4}-\frac{3+2x}{10}=x+\frac{1-x}{5}\)
\(c,\frac{2x}{3}+\frac{3x-5}{4}=\frac{3\left(2x-1\right)}{2}-\frac{7}{6}\)
\(d,\frac{6x+5}{2}-\frac{10x+3}{4}=2x+\frac{2x+1}{2}\)
\(e,\left(x-4\right)\left(x+4\right)-2\left(3x-2\right)=\left(x-4\right)^2\)
Bái 3. Thực hiện phép tính
A=\(\frac{4x^3}{x^4-16}-\frac{1}{x+2}+\frac{2x}{x^2+4}-\frac{1}{x-2}\\ \)
B= \(\frac{1}{x-1}+\frac{2x+3}{\left(x+1\right)^2}-\frac{1}{\left(x+1\right)^2}-\frac{3x-2}{x^2-1}\)
C= \(\left(1+\frac{1}{x}\right)\left(1+\frac{1}{x+1}\right)\left(1+\frac{1}{x+2}\right)...\left(1+\frac{1}{x+9}\right)\)
Thực hiện phép tính:
a)\(\frac{2x+6}{3x^2-x}:\frac{x^2+3x}{1-3x}\)
b)\(\frac{x+3}{x}-\frac{x}{x-3}+\frac{9}{x^2-3x}\)
c)\(\frac{x+3}{x^2-1}-\frac{1}{x^2+x}\)
d)\(\frac{1}{3x-2}-\frac{4}{3x+2}-\frac{-10x+8}{9x^2-4}\)
e)\(\frac{3}{2x^2+2x}+\frac{2x-1}{x^2-1}-\frac{2}{x}\)
f)\(\left(\frac{9}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)
g)\(\frac{8}{\left(x^2+3\right)\left(x^2-1\right)}+\frac{2}{x^2+3}+\frac{1}{x+1}\)
Thực hiện phép tính:
\(a.\left(x+1\right)\left(2x-3\right)+\left(x+2\right)^2-3x^2-3x\)
\(b.\left(x^2+2x-3\right):\left(x+1\right)+x^2-3x-2\)
\(c.\frac{1}{xy-x^2}-\frac{1}{y^2-xy}\)
\(d.\frac{x-1}{x^2-5x+4}-\frac{4}{x^2-4x}\)
Bài 1: rút gọn phân thức
a) \(\frac{14xy^2\left(2x-3y\right)}{21x^2y\left(2x-3y\right)^2}\)
b) \(\frac{8xy\left(3x-1\right)^2}{12x^3\left(1-3x\right)}\)
c) \(\frac{20x^2-45}{\left(2x+3\right)^2}\)
d) \(\frac{5x^2-10xy}{2\left(2y-x\right)^3}\)
e) \(\frac{80x^3-125x}{3\left(x-3\right)-\left(x-3\right)\left(8-4x\right)}\)
f) \(\frac{9-\left(x+5\right)^2}{x^2+4x+4}\)
g) \(\frac{32x-8x^2+2x^3}{x^3+64}\)
h) \(\frac{5x^3+5x}{x^4-1}\)
Bài 2: Quy đồng mẫu thức của các phân thức sau
a) \(\frac{7x-1}{2x^2+6x};\frac{5-3x}{x^2-9}\)
b) \(\frac{x+1}{x-x^2};\frac{x+2}{2-4x+2x^2}\)
c) \(\frac{4x^2-3x+5}{x^3-1};\frac{2x}{x^2+x+1};\frac{6}{x-1}\)
d) \(\frac{7}{5x};\frac{4}{x-2y};\frac{x-y}{8y^2-2x^2}\)
Giải các phương trình sau:
a) \(\frac{x+5}{x^2-5x}-\frac{x+25}{2x^2-50}=\frac{x-5}{2x^2+10x}\).
b) \(\frac{1}{3-x}-\frac{1}{x+1}=\frac{x}{x-3}-\frac{\left(x-1\right)^2}{x^2-2x-3}\).
c) \(\frac{x+1}{x^2+x+1}-\frac{x-1}{x^2-x+1}=\frac{2\left(x+2\right)^2}{x^6-1}\).
d) \(\frac{x}{x-3}-\frac{x}{x-5}=\frac{x}{x-4}-\frac{x}{x-6}\).
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, \(\frac{1}{x^2+3x+2}-\frac{2x}{x^2+4x^2+4x}+\frac{1}{x^2+5x+6}\)