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Simplify the rational expression.

2q^(2)-qr-3r^(2)÷2q^(2)-9qr+9r^(2)

(q+r)(q+3r)
Cannot be simplified

(q+r)(q-3r)

(q-r)(q+3r)

Simplify the rational expression. $\newline$ $2 q^{2}-q r-3 r^{2} \div 2 q^{2}-9 q r+9 r^{2}$ $\newline$ $(q+r)(q+3 r)$ $\newline$ Cannot be simplified $\newline$ $(q+r)(q-3 r)$ $\newline$ $(q-r)(q+3 r)$

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Evaluate integers raised to rational exponents

Full solution

Q. Simplify the rational expression.

\newline

2 q^{2}-q r-3 r^{2} \div 2 q^{2}-9 q r+9 r^{2}

\newline

(q+r)(q+3 r)

\newline

Cannot be simplified

\newline

(q+r)(q-3 r)

\newline

(q-r)(q+3 r)

Factor Numerator: Factor the numerator $2q^2 - qr - 3r^2$ . $\newline$ $2q^2 - qr - 3r^2 = (2q + 3r)(q - r)$
Factor Denominator: Factor the denominator $2q^2 - 9qr + 9r^2$ . $\newline$ $2q^2 - 9qr + 9r^2 = (q - 3r)^2$
Write Fraction: Write the expression as a fraction with the factored numerator and denominator. $\newline$ $(2q + 3r)(q - r) \div (q - 3r)^2$
Cancel Common Factors: Cancel out common factors from the numerator and the denominator. $\newline$ There are no common factors to cancel out.
Final Answer: The expression cannot be simplified further. $\newline$ Final answer: \(2q + $3$ r)(q - r) \div (q - $3$ r)^ $2$ \

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