Question

সমাধান সেট নির্ণয় কর: $\frac{1}{x}+\frac{1}{x+1}=\frac{2}{x-1}$

Answer 1

$\frac{1}{x}+\frac{1}{x+1}=\frac{2}{x-1}$

বা, $\frac{1\left(x+1\right)+x}{x\left(x+1\right)}=\frac{2}{x-1}$

বা, $\frac{x+1+x}{x\left(x+1\right)}=\frac{2}{x-1}$

বা, $\frac{2x+1}{x\left(x+1\right)}=\frac{2}{x-1}$

বা, $\left(2x+1\right)\left(x-1\right)=2\cdot x\left(x+1\right)$

বা, $x\left(2x+1\right)-1\left(2x+1\right)=2x\left(x+1\right)$

বা, $2x^2+x-2x-1=2x^2+2x$

বা, $2x^2+x-2x-2x^2-2x=1$

বা, $-3x=1$

$\therefore x=-\frac13$

সুতরাং নির্ণেয় সমাধান সেট $S=\left\{-\frac13\right\}$ [Answer]