Question

\(\frac{1}{X^2+3x+2}\)+\(\frac{1}{x^2+5x+6}\)=\(\frac{1}{x+3}\)

Answer 1

\(\frac{1}{x^2+3x+2}+\frac{1}{x^2+5x+6}=\frac{1}{x+3}\) \(Đkxđ:.............\)

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

\(\Leftrightarrow x+3+x+1=\left(x+2\right)\left(x+1\right)\)

\(\Leftrightarrow2x+4=x^2+3x+2\)

\(\Leftrightarrow2x+4-x^2-3x-2=0\)

\(\Leftrightarrow x^2+x-2=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=1\left(tmđk\right)\\x=-2\left(ktmđk\right)\end{matrix}\right.\)

Vậy \(S=\left\{1\right\}\)