Question

সমাধান কর: $\frac{4}{2x+1}+\frac{9}{3x+2}=\frac{25}{5x+4}$

Answer 1

$\frac{4}{2x+1}+\frac{9}{3x+2}=\frac{25}{5x+4}$

বা, $\frac{4}{2x+1}+\frac{9}{3x+2}=\frac{10+15}{5x+4}$

বা, $\frac{4}{2x+1}+\frac{9}{3x+2}=\frac{10}{5x+4}+\frac{15}{5x+4}$

বা, $\frac{4}{2x+1}-\frac{10}{5x+4}=\frac{15}{5x+4}-\frac{9}{3x+2}$

বা, $\frac{4\left(5x+4\right)-10\left(2x+1\right)}{\left(2x+1\right)\left(5x+4\right)}=\frac{15\left(3x+2\right)-9\left(5x+4\right)}{\left(5x+4\right)\left(3x+2\right)}$

বা, $\frac{20x+16-20x-10}{\left(2x+1\right)\left(5x+4\right)}=\frac{45x+30-45x-36}{\left(5x+4\right)\left(3x+2\right)}$

বা, $\frac{6}{\left(2x+1\right)\left(5x+4\right)}=\frac{-6}{\left(5x+4\right)\left(3x+2\right)}$

বা, $\frac{1}{\left(2x+1\right)}=\frac{-1}{\left(3x+2\right)}$

[উভয় পক্ষকে $\frac{\left(5x+4\right)}{6}$ দ্বারা গুণ করে]

বা, $\left(3x+2\right)=-\left(2x+1\right)$

বা, $3x+2=-2x-1$

বা, $3x+2x=-2-1$

বা, $5x=-3$

$\therefore x=-\frac35$

সুতরাং নির্ণেয় সমাধান $x=-\frac35$ [Answer]