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! To solve $\frac{6}{x - 2}$ = 3, multiply both sides by (x - 2) to eliminate the denominator. This gives 6 = 3(x - 2). Simplify and solve for x: 6 = 3x - 6, then 12 = 3x, so x = 4.

Feedback: Not quite! Combine the terms with the common denominator x: $\frac{2}{x}$ + 3 = $\frac{8}{x}$ becomes $3 = \frac{8 - 2}{x}$. Simplify to $3 = \frac{6}{x}$, then multiply through by x: 3x = 6, giving $x = 2$.

Feedback: Not quite! Start by multiplying both sides by (x - 3): 32 = 16(x - 3). Distribute: 32 = 16x - 48. Add 48 to both sides: 80 = 16x. Divide by 16 to get x = 5.

Feedback: Not quite! Multiply both sides by (x - 1) to eliminate the fraction: 50(3x + 2) = 250(x - 1). Simplify and solve: 150x + 100 = 250x - 250, leading to x = 3.5.