Subjects algebra

Solve Rational Equation 19Ba0B

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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:** $$\mathbb{R} - \{0\}$$