\(\frac{2}{x-14}\) -\(\frac{5}{x-13}\)= \(\frac{2}{x-9}\)- \(\frac{5}{x-11}\)
ĐKXĐ : x\(\ne\)14;13;9;11
(=) \(\frac{2}{x-14}\)- \(\frac{5}{x-13}\)= \(\frac{2}{x-9}\)-\(\frac{5}{x-11}\)
(=) \(\frac{2}{x-14}\)-\(\frac{2}{x-9}\)=\(\frac{5}{x-13}\)-\(\frac{5}{x-11}\)
(=) \(\frac{2\left(x-9\right)}{\left(x-14\right)\left(x-9\right)}\)-\(\frac{2\left(x-14\right)}{\left(x-14\right)\left(x-9\right)}\)=\(\frac{5\left(x-11\right)}{\left(x-13\right)\left(x-11\right)}\)-\(\frac{5\left(x-13\right)}{\left(x-13\right)\left(x-11\right)}\)
(=) \(\frac{2x-18-2x+28}{\left(x-14\right)\left(x-9\right)}\)=\(\frac{5x-55-5x+65}{\left(x-13\right)\left(x-11\right)}\)
(=) \(\frac{10}{\left(x-14\right)\left(x-9\right)}\)=\(\frac{10}{\left(x-13\right)\left(x-11\right)}\)
=) ( x - 14 ) ( x - 9 ) = ( x - 13 ) ( x - 11 )
(=) x2 - 9x - 14x + 126 = x2 - 13x - 11x + 143
(=) x - 17 = 0
(=) x = 17
Vậy phương trình có nghiệm là: x = 17
