Solving Rational Equations

Multiply both sides of the equation by $x$ to clear the denominator: $\frac{4}{x}\times x=2\times x$. This simplifies to $4=2x$. Now divide both sides by 2: $x=\frac{4}{2}=2$.

Multiply both sides by $(x+3)$ to eliminate the denominator: $5=x+3$. Now subtract 3 from both sides: $x=2$.

Multiply both sides by $(x-2)$ to eliminate the denominator: $6=3(x-2)$. Expand: $6=3x-6$. Add 6 to both sides: $12=3x$. Finally, divide by 3: $x=4$.

Multiply both sides by $x$ to eliminate the denominators: $x\left(\frac{2}{x}+3\right)=x\left(\frac{8}{x}\right)$. This simplifies to $2+3x=8$. Subtract 2 from both sides: $3x=6$. Divide by 3: $x=2$.

Divide both sides by 16 to get $\frac{2}{x-3}=1$. Multiply both sides by $(x-3)$: $2=x-3$. Add 3 to both sides: $x=5$.

Divide both sides by 50: $\frac{3x+2}{x-1}=5$. Multiply both sides by $(x-1)$: $3x+2=5(x-1)$. Expand: $3x+2=5x-5$. Subtract $3x$ from both sides: $2=2x-5$. Add 5 to both sides: $7=2x$. Divide by 2: $x=\frac{7}{2}=3.5$.