Question

Giải phương Trình : 1/(x^2+4x+3)+1/(x^2+8x+15)=1/6

Answer 1

b) ĐKXĐ:\(\left\{{}\begin{matrix}x^2+4x+3\ne0\\x^2+8x+15\ne0\end{matrix}\right.=>\left\{{}\begin{matrix}x\ne-1\\x\ne-3\end{matrix}\right.\)

1/x²+4x+3+1/x²+8x+15=16

⇔1(x+1)(x+3)+1(x+3)(x+5)=16

⇔(x+5)+(x+1)(x+1)(x+3)(x+5)=16

⇔2(x+3)(x+1)(x+3)(x+5)=16

<=>(x+1)(x+5)=12

<=>x²+6x−7=0

<=>(x−1)(x+7)=0

<=>\(\left[{}\begin{matrix}x-1=0\\x+7=0\end{matrix}\right.< =>\left[{}\begin{matrix}x=1\left(nh\text{ậ}n\right)\\x=-7\left(nh\text{ậ}n\right)\end{matrix}\right.\)

S=\(\left\{1;-7\right\}\)