Question

\(\frac{2}{x-14}-\frac{5}{x-13}=\frac{2}{x-9}-\frac{5}{x-11}\)

Answer 1

\(\frac{2}{x-14}-\frac{5}{x-13}=\frac{2}{x-9}-\frac{5}{x-11}.\) \(\left(ĐKXĐ:x\ne14;13;11;9\right)\)

\(\Leftrightarrow\frac{2}{x-14}-\frac{2}{x-9}=\frac{5}{x-13}-\frac{5}{x-11}\)

\(\Leftrightarrow\frac{10}{\left(x-14\right)\left(x-9\right)}=\frac{10}{\left(x-13\right)\left(x-11\right)}\)

\(\Rightarrow\left(x-14\right)\left(x-9\right)=\left(x-13\right)\left(x-11\right)\)

\(\Leftrightarrow x^2-23x+126=x^2-24x+143\)

\(\Leftrightarrow x=17\left(tm\right)\)

Vậy phương trình có tập nhiệm \(S=\left\{17\right\}\)