Question

giải pt \(\frac{x-a}{bc}+\frac{x-b}{ca}+\frac{x-c}{ab}=2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)

Answer 1

\(\frac{x-a}{bc}+\frac{x-b}{ac}+\frac{x-c}{ab}=2\left(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\right)\)

\(\frac{x-a}{bc}+\frac{x-b}{ac}+\frac{x-c}{ab}=\frac{2}{a}+\frac{2}{b}+\frac{2}{c}\)

\(\frac{ax-a^2+bx-b^2+cx-c^2}{abc}=2\left(\frac{ab+bc+ac}{abc}\right)\)

\(ax-a^2+bx-b^2+cx-c^2=2\left(ab+bc+ac\right)\)

\(x\left(a+b+c\right)-\left(a^2+b^2+c^2\right)=2\left(ab+bc+ac\right)\)

\(x\left(a+b+c\right)=a^2+b^2+c^2+2ab+2bc+2ac\)

\(x=a+b+c\)