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Simplify the rational expression. $\newline$ $\frac{2q^{2}-qr-3r^{2}}{2q^{2}-9qr+9r^{2}}$ $\newline$ $(q+r)/(k+3r)$ $\newline$ Cannot be simplified $\newline$ $(a+r)(q-3r)$ $\newline$ $(q+r)(q+3r)$

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Simplify rational expressions

Full solution

Q. Simplify the rational expression.

\newline

\frac{2q^{2}-qr-3r^{2}}{2q^{2}-9qr+9r^{2}}

\newline

(q+r)/(k+3r)

\newline

Cannot be simplified

\newline

(a+r)(q-3r)

\newline

(q+r)(q+3r)

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 $2q^2 - 9qr + 9r^2$ . $\newline$ $2q^2 - 9qr + 9r^2 = (q - 3r)(2q - 3r)$
Write Expression: Now, write the expression with factored numerator and denominator. $\newline$ $(2q + 3r)(q - r) \div (q - 3r)(2q - 3r)$
Cancel Common Factors: Cancel out the common factors. $\newline$ There are no common factors to cancel out.

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