\(\frac{\left(x-2\right)^2}{3}-\frac{\left(2x-3\right)\cdot\left(x+3\right)}{8}+\frac{\left(x-4\right)^2}{6}\)
\(=\frac{x^2-4x+4}{3}-\frac{2x^2+3x-9}{8}+\frac{x^2-8x+16}{6}\)
\(=\frac{8x^2-32x+16}{24}-\frac{6x^2+9x-27}{24}+\frac{4x^2-32x+64}{24}\)
\(=\frac{8x^2-32x+16-6x^2-9x+27+4x^2-32x+64}{24}\)
\(=\frac{6x^2-73x+107}{24}\)
a) \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)
b)\(\frac{x+2}{x-2}-\frac{1}{x}=\frac{2}{x\left(x-2\right)}\)
c)\(\frac{x +1}{x-2}+\frac{x-1}{x +2}=\frac{2\left(x^{2^{ }}+2\right)}{x^2-4}\)
d)(2x+3)\(\left(\frac{3x+8}{2-7x}+1\right)=\left(x-5\right)\left(\frac{3x+8}{2-7x}+1\right)\)
\(1.\frac{1}{x^2-2x+2}+\frac{2}{x^2-2x+3}=\frac{6}{x^2-2x+4}
\)
2.\(\frac{2x^4}{\left(x+1\right)^2}-\frac{5x^2}{x+1}+2=0\)
3.\(\left(x+\frac{1}{x}\right)^2-6\left(x+\frac{1}{x}\right)+8=0\)
4.\(\left(x^2+\frac{1}{x^2}\right)-4\left(x+\frac{1}{x}\right)+6=0\)
5.\(\frac{2x}{3x^2-x+2}-\frac{7x}{3x^2+5x+2}=1\)
26 ,giải phương trình.
a,\(\frac{1}{x-1}+\frac{2}{x^2+x+1}=\frac{3x^2}{x^3-1}\)
b,\(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
c,\(\frac{x-1}{x+2}+\frac{x-2}{x+1}=\frac{2\left(x^2+2\right)}{x^2-4}\)
d,\(\frac{3}{5x-1}+\frac{2}{3-5x}=\frac{4}{\left(1-5x\right)\left(x-3\right)}\)
Giai phuong trinh:
a)\(\frac{4+9x}{9x^21}=\frac{3}{3x+1}-\frac{2}{1-3x}\)
b)\(\frac{2x-3}{x+1}+\frac{x^2-5x+10}{\left(x+1\right)\left(x-3\right)}=\frac{3x-5}{x-3}\)
c)\(\frac{x\left(x+4\right)}{2x-3}=\frac{x^2+4}{2x-3}+1-\frac{2}{3-2x}\)
d)\(\frac{1}{x+2}+\frac{x}{x-3}=1-\frac{5x}{\left(x+2\right)\left(3-x\right)}-\frac{1}{x+2}\)
tìm đkxđ của phân thức : \(\frac{2x}{x+1}\)=\(\frac{x^2-x+8}{\left(x+1\right)\left(x-4\right)}\)
\(\frac{x}{2x-6}\)+\(\frac{x}{2x+2}\)-\(\frac{2x}{\left(x+1\right)\left(x-3\right)}\)=0
\(\frac{x}{2\left(x-3\right)}+\frac{x}{2\left(x+1\right)}=\frac{2x}{\left(x+1\right)\left(x-3\right)}\)
Giari các phương trình sau.
a. \(\frac{1}{x}+\frac{1}{x+10}=\frac{1}{12}\)
b. \(\frac{x+3}{x-3}-\frac{1}{x}=\frac{3}{x\left(x-3\right)}\)
c. \(\frac{3}{x+2}-\frac{2}{x-2}+\frac{8}{x^2-4}=0\)
d. \(\frac{3}{x+2}-\frac{2}{x-3}=\frac{8}{\left(x-3\right)\left(x+2\right)}\)
e. \(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)
f. \(\frac{x}{x+1}-\frac{2x-3}{1-x}=\frac{3x^2+5}{x^2-1}\)
g. \(\frac{5}{x+7}+\frac{8}{2x+14}=\frac{3}{2}\)
h. \(\frac{x-1}{x}-\frac{1}{x+1}=\frac{2x-1}{x^2+x}\)
Giải phương trình sau:
\(\frac{4x^2-\left(x-3\right)^2}{9\left(x^2-1\right)}-\frac{x^2-9}{\left(2x+3\right)^2-x^2}+\frac{\left(2x-3\right)^2-x^2}{4x^2-\left(x+3\right)^2}=1\)
\(\frac{x}{2x+6}-\frac{x}{2x+2}=\frac{3x+2}{\left(x+1\right)\left(x+3\right)}\)