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2q^(2)-qr-3r^(2)÷2q^(2)-9qr+9r^(2)

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

(a+r)(a-3r)

(a-r)(a+3r)

2q2qr3r2÷2q29qr+9r2 2 q^{2}-q r-3 r^{2} \div 2 q^{2}-9 q r+9 r^{2} \newline(q+r)(q+3r) (q+r)(q+3 r) \newlineCannot be simplified\newline(a+r)(a3r) (a+r)(a-3 r) \newline(ar)(a+3r) (a-r)(a+3 r)

Full solution

Q. 2q2qr3r2÷2q29qr+9r2 2 q^{2}-q r-3 r^{2} \div 2 q^{2}-9 q r+9 r^{2} \newline(q+r)(q+3r) (q+r)(q+3 r) \newlineCannot be simplified\newline(a+r)(a3r) (a+r)(a-3 r) \newline(ar)(a+3r) (a-r)(a+3 r)
  1. Check Common Factor: Check if the numerator and denominator have a common factor.\newlineNumerator: 2q2qr3r22q^2 - qr - 3r^2\newlineDenominator: 2q29qr+9r22q^2 - 9qr + 9r^2
  2. Factor Numerator: Factor both the numerator and the denominator.\newlineNumerator: 2q2qr3r2=(2q+3r)(qr)2q^2 - qr - 3r^2 = (2q + 3r)(q - r)\newlineDenominator: 2q29qr+9r2=(q3r)(2q3r)2q^2 - 9qr + 9r^2 = (q - 3r)(2q - 3r)

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