Solve Rational Equation 19Ba0B
1. **State the problem:** Solve the equation $$\frac{2}{y} + \frac{8}{y} - \frac{1}{y} = 9$$ for $y$.
2. **Combine like terms:** Since all terms on the left have the same denominator $y$, combine the numerators:
$$\frac{2 + 8 - 1}{y} = 9$$
which simplifies to
$$\frac{9}{y} = 9$$
3. **Isolate $y$:** Multiply both sides by $y$ to get rid of the denominator:
$$9 = 9y$$
4. **Solve for $y$:** Divide both sides by 9:
$$y = 1$$
5. **Check domain restrictions:** Since $y$ is in the denominator, $y \neq 0$ to avoid division by zero. Our solution $y=1$ is valid.
**Final answer:**
$$y = 1$$
**Domain:**
$$\mathbb{R} - \{0\}$$