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Simplify. Write your answer using whole numbers and variables. $\newline$ $\frac{9x^2 + 2x}{9x + 2}$

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Convert equations of parabolas from general to vertex form

Full solution

Q. Simplify. Write your answer using whole numbers and variables.

\newline

\frac{9x^2 + 2x}{9x + 2}

Identify expression: Identify the expression to be simplified. $\newline$ The expression given is $9x^2 + \frac{2x}{9x} + 2$ . We need to simplify this expression by combining like terms and simplifying any fractions if possible.
Simplify fraction: Simplify the fraction in the expression. $\newline$ The fraction in the expression is $\frac{2x}{9x}$ . Since $x$ is in both the numerator and the denominator, we can simplify this fraction by dividing both the numerator and the denominator by $x$ . $\newline$ $\frac{2x}{9x} = \left(\frac{2}{x}\right) \cdot \left(\frac{x}{9x}\right) = \frac{2}{9}$
Rewrite expression: Rewrite the expression with the simplified fraction. $\newline$ Now that we have simplified the fraction, we can rewrite the expression as: $\newline$ $9x^2 + \frac{2}{9} + 2$
Combine constant terms: Combine the constant terms. $\newline$ The constant terms in the expression are $\frac{2}{9}$ and $2$ . We can combine these by finding a common denominator and adding them together. $\newline$ $\frac{2}{9} + 2 = \frac{2}{9} + \frac{18}{9} = \frac{20}{9}$
Write final expression: Write the final simplified expression. $\newline$ The final simplified expression, with the combined constant terms, is: $\newline$ $9x^2 + \frac{20}{9}$

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