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1)
![frac{a}{b} - 1 = frac{a}{b} - frac{b}{b} = frac{a - b}{b} frac{a}{b} - 1 = frac{a}{b} - frac{b}{b} = frac{a - b}{b}](https://tex.z-dn.net/?f=+frac%7Ba%7D%7Bb%7D++-++1+%3D++frac%7Ba%7D%7Bb%7D++-+++frac%7Bb%7D%7Bb%7D++%3D++frac%7Ba+-+b%7D%7Bb%7D+)
2)
![frac{8}{ {x}^{2} } - frac{3}{x} + 2 = frac{8}{ {x}^{2} } - frac{3x}{ {x}^{2} } + frac{2 {x}^{2} }{ {x}^{2} } = frac{8 - 3x + 2 {x}^{2} }{ {x}^{2} } frac{8}{ {x}^{2} } - frac{3}{x} + 2 = frac{8}{ {x}^{2} } - frac{3x}{ {x}^{2} } + frac{2 {x}^{2} }{ {x}^{2} } = frac{8 - 3x + 2 {x}^{2} }{ {x}^{2} }](https://tex.z-dn.net/?f=+frac%7B8%7D%7B+%7Bx%7D%5E%7B2%7D+%7D++-++frac%7B3%7D%7Bx%7D++%2B+2+%3D++frac%7B8%7D%7B+%7Bx%7D%5E%7B2%7D+%7D++-++frac%7B3x%7D%7B+%7Bx%7D%5E%7B2%7D+%7D++%2B++frac%7B2+%7Bx%7D%5E%7B2%7D+%7D%7B+%7Bx%7D%5E%7B2%7D+%7D++%3D++frac%7B8+-+3x+%2B+2+%7Bx%7D%5E%7B2%7D+%7D%7B+%7Bx%7D%5E%7B2%7D+%7D+)
3)
![5 - frac{4m + 5n}{n} = frac{5n}{n} - frac{4m + 5n}{n} = frac{5n - (4m + 5n)}{n} = frac{5n - 4m - 5n}{n} = - frac{4m}{n} 5 - frac{4m + 5n}{n} = frac{5n}{n} - frac{4m + 5n}{n} = frac{5n - (4m + 5n)}{n} = frac{5n - 4m - 5n}{n} = - frac{4m}{n}](https://tex.z-dn.net/?f=5+-++frac%7B4m+%2B+5n%7D%7Bn%7D++%3D++frac%7B5n%7D%7Bn%7D++-++frac%7B4m+%2B+5n%7D%7Bn%7D++%3D++frac%7B5n+-+%284m+%2B+5n%29%7D%7Bn%7D++%3D++frac%7B5n+-+4m+-+5n%7D%7Bn%7D++%3D++-++frac%7B4m%7D%7Bn%7D+)
4)
![frac{4c + 3}{c - 1} - 3 = frac{4c + 3}{c - 1} - frac{3(c - 1)}{c - 1} = frac{4c + 3 - 3(c - 1)}{c - 1} = frac{4c + 3 - 3c + 3}{c - 1} = frac{c + 6}{c - 1} frac{4c + 3}{c - 1} - 3 = frac{4c + 3}{c - 1} - frac{3(c - 1)}{c - 1} = frac{4c + 3 - 3(c - 1)}{c - 1} = frac{4c + 3 - 3c + 3}{c - 1} = frac{c + 6}{c - 1}](https://tex.z-dn.net/?f=+frac%7B4c+%2B+3%7D%7Bc+-+1%7D++-+3+%3D++frac%7B4c+%2B+3%7D%7Bc+-+1%7D++-++frac%7B3%28c+-+1%29%7D%7Bc+-+1%7D++%3D++frac%7B4c+%2B+3+-+3%28c+-+1%29%7D%7Bc+-+1%7D++%3D++frac%7B4c+%2B+3+-+3c+%2B+3%7D%7Bc+-+1%7D++%3D++frac%7Bc+%2B+6%7D%7Bc+-+1%7D+)
5)
![frac{ {a}^{2} + {b}^{2} }{2a - b} + 2a + b = frac{ {a}^{2} + {b}^{2} }{2a - b} + frac{(2a + b)(2a - b)}{2a - b} = frac{ {a}^{2} + {b}^{2} }{2a - b} + frac{4 {a}^{2} - {b}^{2} }{2a - b} = frac{ {a}^{2} + {b}^{2} + 4 {a}^{2} - {b}^{2} }{2a - b} = frac{5 {a}^{2} }{2a - b} frac{ {a}^{2} + {b}^{2} }{2a - b} + 2a + b = frac{ {a}^{2} + {b}^{2} }{2a - b} + frac{(2a + b)(2a - b)}{2a - b} = frac{ {a}^{2} + {b}^{2} }{2a - b} + frac{4 {a}^{2} - {b}^{2} }{2a - b} = frac{ {a}^{2} + {b}^{2} + 4 {a}^{2} - {b}^{2} }{2a - b} = frac{5 {a}^{2} }{2a - b}](https://tex.z-dn.net/?f=+frac%7B+%7Ba%7D%5E%7B2%7D++%2B++%7Bb%7D%5E%7B2%7D+%7D%7B2a+-+b%7D++%2B+2a+%2B+b+%3D++frac%7B+%7Ba%7D%5E%7B2%7D++%2B++%7Bb%7D%5E%7B2%7D+%7D%7B2a+-+b%7D++%2B++frac%7B%282a+%2B+b%29%282a+-+b%29%7D%7B2a+-+b%7D++%3D++frac%7B+%7Ba%7D%5E%7B2%7D++%2B++%7Bb%7D%5E%7B2%7D+%7D%7B2a+-+b%7D++%2B++frac%7B4+%7Ba%7D%5E%7B2%7D++-++%7Bb%7D%5E%7B2%7D+%7D%7B2a+-+b%7D++%3D++frac%7B+%7Ba%7D%5E%7B2%7D+%2B++%7Bb%7D%5E%7B2%7D+%2B+4+%7Ba%7D%5E%7B2%7D++-++%7Bb%7D%5E%7B2%7D+++%7D%7B2a+-+b%7D++%3D++frac%7B5+%7Ba%7D%5E%7B2%7D+%7D%7B2a+-+b%7D+)
6)
![m - frac{25}{m - 5} - 5 = m - 5 - frac{25}{m - 5} = frac{ {(m - 5)}^{2} }{m - 5} - frac{25}{m - 5} = frac{ {(m - 5)}^{2} - 25}{m - 5} = frac{ {m}^{2} - 10m + 25 - 25 }{m - 5} = frac{ {m}^{2} - 10m}{m - 5} m - frac{25}{m - 5} - 5 = m - 5 - frac{25}{m - 5} = frac{ {(m - 5)}^{2} }{m - 5} - frac{25}{m - 5} = frac{ {(m - 5)}^{2} - 25}{m - 5} = frac{ {m}^{2} - 10m + 25 - 25 }{m - 5} = frac{ {m}^{2} - 10m}{m - 5}](https://tex.z-dn.net/?f=m+-++frac%7B25%7D%7Bm+-+5%7D++-+5+%3D+m+-+5+-++frac%7B25%7D%7Bm+-+5%7D++%3D++frac%7B+%7B%28m+-+5%29%7D%5E%7B2%7D+%7D%7Bm+-+5%7D++-++frac%7B25%7D%7Bm+-+5%7D++%3D++frac%7B+%7B%28m+-+5%29%7D%5E%7B2%7D++-+25%7D%7Bm+-+5%7D++%3D++frac%7B+%7Bm%7D%5E%7B2%7D+-+10m+%2B+25+-+25+%7D%7Bm+-+5%7D++%3D++frac%7B+%7Bm%7D%5E%7B2%7D++-+10m%7D%7Bm+-+5%7D+)
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