Solving Rational Equations

Feedback: Not quite! 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: $x = \frac{4}{2} = 2$.

Feedback: Not quite! Multiply both sides by $(x+3)$ to eliminate the denominator: $\frac{5}{x+3} \times (x+3) = 1 \times (x+3)$. This simplifies to: $5 = x + 3$. Now subtract 3 from both sides: $x = 2$.

Feedback: Not quite! Start by multiplying both sides of the equation by $(x - 2)$ to eliminate the denominator: $6 = 3(x - 2)$. Now expand the right side: $6 = 3x - 6$. Add 6 to both sides: $12 = 3x$. Finally, divide by 3: $x = \frac{12}{3} = 4$.

Feedback: Not quite! Start by multiplying both sides of the equation by $x$ to eliminate the denominators: $x(\frac{2}{x} + 3) = x(\frac{8}{x})$, which simplifies to $2 + 3x = 8$. Now subtract 2 from both sides to get $3x = 6$, and finally divide both sides by 3 to find $x = 2$.

Feedback: Not quite! Start by dividing both sides of the equation by $16$ to get: $ \frac{2}{x - 3} = 1$. Then, multiply both sides by $(x - 3)$ to eliminate the denominator: $2 = x - 3$. Add $3$ to both sides to isolate $x$: $x = 5$.

Feedback: Not quite! Start by dividing both sides of the equation by $50$ to get: $ \frac{3x + 2}{x - 1} = 5$. Then, multiply both sides by $(x - 1)$ to eliminate the denominator: $3x + 2 = 5(x - 1)$. Expand the right side: $3x + 2 = 5x - 5$. Subtract $3x$ from both sides: $2 = 2x - 5$. Add $5$ to both sides: $7 = 2x$. Finally, divide by $2$: $x = \frac{7}{2} = 3.5$.