Question

Розв'яжіть рівняння
4/х²-25 - 2/x²-5x+x-6/x²+5x =0

Answer 1

$\displaystyle\bf\\\frac{4}{x^{2} -25} -\frac{2}{x^{2} -5x} +\frac{x-6}{x^{2} +5x} =0\\\\\\\frac{4}{(x-5)(x+5)} -\frac{2}{x\cdot(x-5)} +\frac{x-6}{x\cdot(x+5)} =0\\\\\\\frac{4\cdot x-2\cdot(x+5)+(x-6)\cdot(x-5)}{x(x-5)(x+5)}=0\\\\\\\frac{4x-2x-10+x^{2} -5x-6x+30}{x(x-5)(x+5)} =0\\\\\\\frac{x^{2} -9x+20}{x(x-5)(x+5)} =0\\\\\\\left \{ {{x^{2} -9x+20=0} \atop {x\neq 0 \ , \ x-5\neq 0 \ , \ x+5\neq 0}} \right.$

$\displaystyle\bf\\\left \{ {{(x-4)(x-5)=0} \atop {x\neq 0 \ , \ x\neq 5 \ , \ x\neq -5}} \right. \\\\\\x-4=0 \ \ \Rightarrow \ \ x=4\\\\x-5=0 \ \ \Rightarrow \ \ x=5 - \ neyd\\\\Otvet \ : \ 4$