2x³+5x²=7x

-7x+5x²+2x³=7x+(-7x)

ta có 7x+(-7x)

-7x + 5x2 + 2x3 = 0

x(-7 + 5x + 2x2) = 0

x[(-7 + -2x)(1 + -1x)] = 0

2x^3 + 5x^2 = 7x

<=> 2x^3 + 5x^2 - 7x = 0

<=> x(2x^2 + 5x - 7) = 0

<=> x(2x^2 + 7x - 2x - 7) = 0

<=> x[x(2x + 7) - (2x + 7)] = 0

<=> x(x - 1)(2x + 7) = 0

<=> x = 0 hoặc x - 1 = 0 hoặc 2x + 7 = 0

<=> x = 0 hoặc x = 1 hoặc x = -7/2

\(\frac{x^3-27}{x^2-9}=0\)

\(\Leftrightarrow x^3-27=0\)

\(\Leftrightarrow x^3=27\)

\(\Leftrightarrow x=\pm3\)

ĐKXĐ :\(x\ne\pm3\)

\(C=A+B=\frac{x^4+1}{x^4-x^3+2x^2-x+1}+\frac{x}{x^2-x+1}\)

\(=\frac{x^4+1}{x^4-x^3+x^2+x^2-x+1}+\frac{x}{x^2-x+1}\)

\(=\frac{x^4+1}{\left(x^2+1\right)\left(x^2-x+1\right)}+\frac{x^3+x}{\left(x^2+1\right)\left(x^2-x+1\right)}\)

\(=\frac{x^4+x^3+x+1}{\left(x^2+1\right)\left(x^2-x+1\right)}=\frac{\left(x^3+1\right)\left(x+1\right)}{\left(x^2+1\right)\left(x^2-x+1\right)}\)

\(=\frac{\left(x+1\right)^2}{x^2+1}\)

\(C=0\Leftrightarrow\frac{\left(x+1\right)^2}{x^2+1}=0\)

\(\Leftrightarrow\left(x+1\right)^2=0\Leftrightarrow x=-1\)

\(P=\frac{x^3+2x^2-5x-6}{x^2+x-6}=\frac{\left(x-2\right)\left(x+3\right)\left(x+1\right)}{\left(x-2\right)\left(x+3\right)}\)

=> x khác 2; x khác -3

không chắc đâu nhé :))

\(ĐKXĐ:x\ne2;x\ne4\)

\(\frac{x-3}{x-2}+\frac{x-2}{x-4}=-1\)

\(\Leftrightarrow\frac{\left(x-3\right)\left(x-4\right)+\left(x-2\right)^2}{\left(x-2\right)\left(x-4\right)}=-1\)

\(\Leftrightarrow\frac{x^2-7x+12+x^2-4x+4}{x^2-6x+8}=-1\)

\(\Leftrightarrow2x^2-11x+16=-x^2+6x-8\)

\(\Leftrightarrow3x^2-17x+24=0\)

\(\Leftrightarrow\left(x-3\right)\left(3x-8\right)=0\)

\(\Leftrightarrow x=3;x=\frac{8}{3}\)

Vậy tập nghiệm của phương trình  là \(S=\left\{3;\frac{8}{3}\right\}\)

\(\left(x+2\right)\left(x+4\right)\left(x+6\right)\left(x+8\right)+2008\)

\(=\left[\left(x+2\right)\left(x+8\right)\right]\left[\left(x+4\right)\left(x+6\right)\right]\)

\(=\left(x^2+10x+16\right)\left(x^2+10x+24\right)+2008\)

Đặt \(x^2+10x+20=t\)

Khi đó phương trình tương đương với:

\(\left(t-4\right)\left(t+4\right)+2008=t^2-16+2008=t^2+1992\)

Không hiểu phân tích ra như thế nào ?????