Kürzen Sie folgenden Bruchterm:
{\displaystyle \quad } 6 x 2 − 5 x + 3 x 2 + 2 x 18 x 3 − 12 x 2 + 2 x {\displaystyle {\frac {6x^{2}-5x+3x^{2}+2x}{18x^{3}-12x^{2}+2x}}}
{\displaystyle \quad } 6 x 2 − 5 x + 3 x 2 + 2 x 18 x 3 − 12 x 2 + 2 x = 9 x 2 − 3 x 18 x 3 − 12 x 2 + 2 x = … {\displaystyle {\frac {6x^{2}-5x+3x^{2}+2x}{18x^{3}-12x^{2}+2x}}={\frac {9x^{2}-3x}{18x^{3}-12x^{2}+2x}}=\dots } {\displaystyle \quad } ⋯ = 3 x ( 3 x − 1 ) 2 x ( 9 x 2 − 6 x + 1 ) = 3 x ( 3 x − 1 ) 1 2 x ( 3 x − 1 ) 2 1 {\displaystyle \dots ={\frac {3x(3x-1)}{2x(9x^{2}-6x+1)}}={\frac {3{\cancel {x}}{\cancelto {1}{(3x-1)}}}{2{\cancel {x}}(3x-1)^{{\cancel {2}}^{1}}}}} {\displaystyle \quad } also 6 x 2 − 5 x + 3 x 2 + 2 x 18 x 3 − 12 x 2 + 2 x = 3 2 ( 3 x − 1 ) {\displaystyle \quad \quad {\frac {6x^{2}-5x+3x^{2}+2x}{18x^{3}-12x^{2}+2x}}={\frac {3}{2(3x-1)}}}
