GIẢI PHƯƠNG TRÌNH
a)\(\frac{1-x}{x+1}+3=\frac{2x+3}{x+1}\)
b)\(\frac{1}{x+1}-\frac{5}{x-2}=\frac{15}{\left(x+1\right)\left(2-x\right)}\)
c)\(\frac{12}{1-9x^2}=\frac{1-3x}{1+3x}-\frac{1+3x}{1-3x}\)
d)\(\frac{x+4}{x^2-3x+2}+\frac{x+1}{x^2-4x+3}=\frac{2x+5}{x^2-4x+3}\)
Rút gọn
a) \(\left(\frac{4}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x^2+3x}-\frac{x}{3x+9}\right)\)
b) \(\left(\frac{2}{x-2}-\frac{2}{x+2}\right).\frac{x^2+4x+4}{8}\)
c) \(\left(\frac{3x}{1-3x}+\frac{2x}{3x+1}\right):\frac{6x^2+10x}{1-6x+9x^2}\)
\(a.\frac{4x-7}{12}-x=\frac{3x}{8}\\ b.\frac{5x-8}{3}=\frac{1-3x}{2}\\ c.\left(\frac{x-1}{\frac{2}{5}}-3\right)-\left(\frac{3x-2}{\frac{5}{4}}-2\right)=1\)
Rút gọn các phân thức:
a)\(\frac{x^4-4x^2+3}{x^4+6x^2-7}\)
b)\(\frac{x^4+x^3-x-1}{x^4+x^3+2x^2+x+1}\)
c)\(\frac{x^3+3x^2-4}{x^3-3x+2}\)
d)\(\frac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}\)
e)\(\frac{\left(x-y\right)^3-3xy\left(x+y\right)+y^3}{x-6y}\)
f)\(\frac{x^2+y^2+z^2-2xy+2xz-2yz}{x^2-2xy+y^2-z^2}\)
\(a,\frac{3x^2-6xy+3y^2}{5x^2-5xy+5y^2}:\frac{10x-10y}{x^3+y^3}\)
\(b,(\frac{x+2}{x+1}-\frac{2x}{x-1}).\frac{3x+3}{x}+\frac{4x^2+x+7}{x^2-x}\)
\(c,\frac{2}{xy}:\left(\frac{1}{x}-\frac{1}{y}\right)-\frac{x^2-y^2}{\left(x-y\right)^2}\)
\(d,\frac{\frac{x-y}{x+y}-\frac{x+y}{x-y}}{1-\frac{x^2}{x^2+y^2}}\)
\(e,\left(\frac{1}{x+1}-\frac{3}{x^3+1}+\frac{3}{x^2-x+1}\right).\frac{3x^2-3x+3}{\left(x+1\right)\left(x+2\right)}+\frac{2x-2}{x^2+2x}\)
giải phương trình sau:
a) \(\frac{3x+2}{3x-2}-\frac{6}{2+3x}=\frac{9x^2}{9x-4}\\\)
b) \(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(x-3\right)}\)
c)\(\frac{3}{1-4x}=\frac{2}{4x+1}-\frac{8+6x}{16x^2-1}\)
d) \(5+\frac{76}{x^2-16}=\frac{2x-1}{x+4}-\frac{3x-1}{4-x}\)
thực hiện phép cộng các phân thức
a)\(\frac{5x-1}{3x^2y}+\frac{x+1}{3x^2y}\)
b)\(\frac{7}{12xy^2}+\frac{11}{18x^3y}\)
c)\(\frac{x}{x+2}+\frac{7x-16}{\left(x+2\right)\left(4x-7\right)}\)
bài 1. giải các phương trình sau
a / \(x =(4x+1) (\frac{3x+7}{3-5x}+1)=(x+4)(\frac{3x+7}{5x-3}-1)\)
b/ \(\left(x^2+3x+1\right)\left(\frac{4x-3}{3x+1}+2\right)=\left(4x+7\right)\left(\frac{4x-3}{3x+1}+2\right)\)1)
bài 2. giải phương trình sau bằng cách đưa về phương trình tích
a/\(\left(4x-5\right)^2-2\left(16x^2-25\right)=0\)
b/ \(\left(4x+3\right)^2=4\left(x^2-2x+1\right)\)
c. \(3x^3-3x^2-6x=0\)
cảm ơn mọi người nhiều lắm !
Rút gọn phân thức:
a) \(\frac{3x^2+1}{3x+1}\) b)\(\frac{25\left(x-1\right)^3}{15\left(1-x\right)}\) c)\(\frac{x^2-xy}{3x^2-3y^2}\) d)\(\frac{x^2+y^2-4x+2xy}{x^2-y^2+4+4x}\)