Giải các phương trình sau:

a) \(x^2+\dfrac{2x}{x-1}=8\)

b) \(\dfrac{x^2+2x+1}{x^2+2x+2}+\dfrac{x^2+2x+2}{x^2+2x+3}=\dfrac{7}{6}\)

c) \(\dfrac{x+4}{x-1}+\dfrac{x-4}{x+1}=\dfrac{x+8}{x-2}+\dfrac{x-8}{x+2}+6\)

d) \(\left(x^2+6x+8\right)\left(x^2+8x+15\right)=24\)

e) \(\left(x^2+x-2\right)\left(x^2+9x+18\right)=28\)

f) \(3\left(-x^2+2x+3\right)^4-26x^2\left(-x^2+2x+3\right)^2-9x^4=0\)

g) \(x^4+6x^3+11x^2+6x+1=0\)

h) \(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2=0\)

i) \(\left(x+2\right)^4+\left(x+8\right)^4=272\)

 1 . \(\left(3x-2\right)\left(x^2-1\right)=\left(9x^2-4\right)\left(x+1\right)\)

2 . \(\frac{7}{8}x-5\left(x-9\right)=\frac{20x+1,5}{6}\)

3 . \(4\left(0,5-1,5x\right)=\frac{5x-6}{3}\)

4 . \(\left(3x-1\right)\left(x^2+2\right)=\left(3x-1\right)\left(7x-10\right)\)

5 . \(\frac{8x^2}{3\left(1-4x^2\right)}+\frac{1}{2x+7}=\frac{6}{x^2-9}\)

PHÂN TÍCH:

a)\(\left(x^2+8x+12\right)\left(x^2+12x+32\right)+16\)

b)\(\left(x^2+6x+8\right)\left(x^2+8x+15\right)-24\)

c)\(\left(x^2-6x+5\right)\left(x^2-10x+21\right)-20\)

d)\(\left(x^2+x-2\right)\left(x^2+9x+18\right)-28\)

e)\(\left(x^2-11x+28\right)\left(x^2-7x+10\right)-72\)

f) \(\left(x^2+5x+6\right)\left(x^2-15x+56\right)-144\)

g)\(\left(x^2-x\right)^2+3\left(x^2-x\right)+2\)

h)\(\left(x^2+5x\right)^2+10x^2+50x+24\)

i)\(x^4+2016x^2+2015x+2016\)

Xác định a, b để \(f\left(x\right)⋮g\left(x\right)\)

a) f(x)= \(2x^3-3x^2+ax+b\) ; \(g\left(x\right)=x^2+x+2\)

b) \(f\left(x\right)=2x^4+ax^2+b\) ; \(g\left(x\right)=x^2-x-3\)

c) \(f\left(x\right)=3x^4-8x^3-10x^2+ax-b\) ; \(g\left(x\right)=3x^2-2x+1\)

d) \(f\left(x\right)=ax^3+bx^2-11x+30\) ; \(g\left(x\right)=x^2-3x-10\)

Xác định a, b để f(x) \(⋮\) g(x)

a) \(f\left(x\right)=2x^3-3x^2+ax+b\) ; \(g\left(x\right)=x^2+x+2\)

b) \(f\left(x\right)=2x^4+2x^2+b\) ; \(g\left(x\right)=x^2-x-3\)

c) \(f\left(x\right)=3x^4-8x^3-10x^2+ax-b\) ; \(g\left(x\right)=3x^2-2x+1\)

d) \(f\left(x\right)=ax^3+bx^2-11x+30\) ; \(g\left(x\right)=x^2-3x-10\)