Oblicz. [(2/3)2 + 2/32 – (1 1/3)2] : [2 1/7 : 1 ½] ma wyjść 0
djpancernikfotk
![\left[\left(\dfrac{2}{3}\right)^2+\dfrac{2}{32}-\left(1\dfrac{1}{3}\right)^2\right]:\left[2\dfrac{1}{7}:1\dfrac{1}{2}\right]=\left[\dfrac{4}{9}+\dfrac{1}{16}-\left(\dfrac{4}{3}\right)^2\right]:\\ :\left[\dfrac{15}{7}:\dfrac{3}{2}\right]=\left[\dfrac{4}{9}+\dfrac{1}{16}-\dfrac{16}{9}\right]:\left[\dfrac{15}{7}\cdot\dfrac{2}{3}\right]=\\ =\left[\dfrac{1}{16}-\dfrac{12}{9}\right] :\left[\dfrac{5}{7}\cdot\dfrac{2}{1}\right]=\left[\dfrac{1}{16}-\dfrac{4}{3}\right]:\dfrac{10}{7}=](https://tex.z-dn.net/?f=%5Cleft%5B%5Cleft%28%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%5E2%2B%5Cdfrac%7B2%7D%7B32%7D-%5Cleft%281%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5E2%5Cright%5D%3A%5Cleft%5B2%5Cdfrac%7B1%7D%7B7%7D%3A1%5Cdfrac%7B1%7D%7B2%7D%5Cright%5D%3D%5Cleft%5B%5Cdfrac%7B4%7D%7B9%7D%2B%5Cdfrac%7B1%7D%7B16%7D-%5Cleft%28%5Cdfrac%7B4%7D%7B3%7D%5Cright%29%5E2%5Cright%5D%3A%5C%5C%0A%3A%5Cleft%5B%5Cdfrac%7B15%7D%7B7%7D%3A%5Cdfrac%7B3%7D%7B2%7D%5Cright%5D%3D%5Cleft%5B%5Cdfrac%7B4%7D%7B9%7D%2B%5Cdfrac%7B1%7D%7B16%7D-%5Cdfrac%7B16%7D%7B9%7D%5Cright%5D%3A%5Cleft%5B%5Cdfrac%7B15%7D%7B7%7D%5Ccdot%5Cdfrac%7B2%7D%7B3%7D%5Cright%5D%3D%5C%5C%0A%3D%5Cleft%5B%5Cdfrac%7B1%7D%7B16%7D-%5Cdfrac%7B12%7D%7B9%7D%5Cright%5D%0A%3A%5Cleft%5B%5Cdfrac%7B5%7D%7B7%7D%5Ccdot%5Cdfrac%7B2%7D%7B1%7D%5Cright%5D%3D%5Cleft%5B%5Cdfrac%7B1%7D%7B16%7D-%5Cdfrac%7B4%7D%7B3%7D%5Cright%5D%3A%5Cdfrac%7B10%7D%7B7%7D%3D "\left[\left(\dfrac{2}{3}\right)^2+\dfrac{2}{32}-\left(1\dfrac{1}{3}\right)^2\right]:\left[2\dfrac{1}{7}:1\dfrac{1}{2}\right]=\left[\dfrac{4}{9}+\dfrac{1}{16}-\left(\dfrac{4}{3}\right)^2\right]:\\ :\left[\dfrac{15}{7}:\dfrac{3}{2}\right]=\left[\dfrac{4}{9}+\dfrac{1}{16}-\dfrac{16}{9}\right]:\left[\dfrac{15}{7}\cdot\dfrac{2}{3}\right]=\\ =\left[\dfrac{1}{16}-\dfrac{12}{9}\right] :\left[\dfrac{5}{7}\cdot\dfrac{2}{1}\right]=\left[\dfrac{1}{16}-\dfrac{4}{3}\right]:\dfrac{10}{7}=")
![=\left[\dfrac{3}{48}-\dfrac{64}{48}\right]\cdot\dfrac{7}{10}=-\dfrac{61}{48}\cdot\dfrac{7}{10}=-\dfrac{427}{480}](https://tex.z-dn.net/?f=%3D%5Cleft%5B%5Cdfrac%7B3%7D%7B48%7D-%5Cdfrac%7B64%7D%7B48%7D%5Cright%5D%5Ccdot%5Cdfrac%7B7%7D%7B10%7D%3D-%5Cdfrac%7B61%7D%7B48%7D%5Ccdot%5Cdfrac%7B7%7D%7B10%7D%3D-%5Cdfrac%7B427%7D%7B480%7D "=\left[\dfrac{3}{48}-\dfrac{64}{48}\right]\cdot\dfrac{7}{10}=-\dfrac{61}{48}\cdot\dfrac{7}{10}=-\dfrac{427}{480}")
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