What is (3x^2-11x+6)/(9x^2-12x+4) ?

The solution to (3x^2-11x+6)/(9x^2-12x+4) is (x-3)/(3x-2)

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simplify (3x^2-11x+6)/(9x^2-12x+4)

simplify

\frac{3 x ^{2} - 11 x + 6}{9 x ^{2} - 12 x + 4}

\frac{x - 3}{3 x - 2}

Solution steps

\frac{3 x ^{2} - 11 x + 6}{9 x ^{2} - 12 x + 4}

Factor

3 x^{2} - 11 x + 6 : (3 x - 2) (x - 3)

= \frac{( 3 x - 2 ) ( x - 3 )}{9 x ^{2} - 12 x + 4}

Factor

9 x^{2} - 12 x + 4 : (3 x - 2)^{2}

= \frac{( 3 x - 2 ) ( x - 3 )}{( 3 x - 2 ) ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(3 x - 2)^{2} = (3 x - 2) (3 x - 2)

= \frac{( 3 x - 2 ) ( x - 3 )}{( 3 x - 2 ) ( 3 x - 2 )}

Cancel the common factor:

3 x - 2

= \frac{x - 3}{3 x - 2}

(- 2 x^{3}) (- 5 x) (- 3 x^{2})

2 x^{3} - x^{2}

\frac{64}{24}

3 - 192

What is (3x^2-11x+6)/(9x^2-12x+4) ?
The solution to (3x^2-11x+6)/(9x^2-12x+4) is (x-3)/(3x-2)