Cho biểu thức

A= \(\left[\frac{3}{2}\left(x^4-\frac{x^4+1}{x^2+1}\right).\frac{x^3-x\left(4x-1\right)-4}{x^7+6x^6-x-6}\right]:\frac{x^2+29x+78}{3x^2+12x-36}\)

a) Rút gọn A

b) Tìm x nguyên để A có giá trị nguyên

Giải các phương trình sau

a) \(\frac{1}{x+1}-\frac{5}{x-2}=\frac{15}{\left(x+1\right)\left(2-x\right)}\)

b) \(\frac{1}{2x-3}-\frac{3}{x\left(2x-3\right)}=\frac{5}{x}\)

c) \(\frac{6}{x-1}-\frac{4}{x-3}=\frac{8}{2x-6}\)

d) \(\frac{3}{\left(x-1\right)\left(x-2\right)}+\frac{2}{\left(x-3\right)\left(x-1\right)}=\frac{1}{\left(x-2\right)\left(x-3\right)}\)

e) \(\frac{1}{x-2}+\frac{5}{x+1}=\frac{3}{2-x}\)

f) \(\frac{5x}{2x+2}+1=-\frac{6}{x+1}\)

g) \(\frac{x+1}{x-1}-\frac{x-1}{x+1}=\frac{4}{x^2-1}\)

h) \(\frac{3x}{x-2}-\frac{x}{x-5}=\frac{3x}{\left(x-2\right)\left(5-x\right)}\)

Giải các phương trình sau

a) \(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}+\frac{x-23}{27}\)

b) \(\left(\frac{x+2}{98}+1\right)+\left(\frac{x+3}{97}+1\right)=\left(\frac{x+4}{96}+1\right)+\left(\frac{x+5}{95}+1\right)\)

c) \(\frac{x+1}{2004}+\frac{x+2}{2003}=\frac{x+3}{2002}+\frac{x+4}{2001}\)

d) \(\frac{201-x}{99}+\frac{203-x}{97}=\frac{205-x}{95}+3=0\)

Giải phương trình

a) \(2x\left(x+5\right)=\left(x+3\right)^2+\left(x-1\right)^2+20\)

b) \(\left(2x-2\right)^3=\left(x+1\right)^2+3\left(x-2\right)\left(x+5\right)\)

c) \(\left(x-1\right)^2+\left(x+3\right)^2=2\left(x-2\right)\left(x+1\right)+38\)

d) \(\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-2\right)-8\)

Giải các phương trình sau

a) \(\left(2x-2\right)^3=\left(x+1\right)^2+3\left(x-2\right)\left(x+5\right)\)

b) \(\left(x-1\right)^2+\left(x+3\right)^2=2\left(x+2\right)+\left(x+1\right)+38\)

c) \(\left(x+2\right)^3-\left(x-2\right)^3=12x\left(x-2\right)-8\)

Tìm giá trị lớn nhất của biểu thức

\(B=\frac{3x^2+9x+17}{3x^2+9x+7}\)