#2
1)
![( \frac{3 {c}^{4} }{7b {m}^{5} } ) = \frac{9 {c}^{8} }{49 {b}^{2} {m}^{10} }](https://tex.z-dn.net/?f=%28+%5Cfrac%7B3+%7Bc%7D%5E%7B4%7D+%7D%7B7b+%7Bm%7D%5E%7B5%7D+%7D+%29+%3D+%5Cfrac%7B9+%7Bc%7D%5E%7B8%7D+%7D%7B49+%7Bb%7D%5E%7B2%7D+%7Bm%7D%5E%7B10%7D+%7D+)
2)
![\frac{m + n}{m - n} + \frac{m}{n} = \frac{n \times (m + n) + m \times (m - n)}{n \times (m - n)} = \frac{mn + {n}^{2} + {m}^{2} - mn }{mn - {n}^{2} } = \frac{ {n}^{2} + {m}^{2} }{mn - {n}^{2} }](https://tex.z-dn.net/?f=+%5Cfrac%7Bm+%2B+n%7D%7Bm+-+n%7D+%2B+%5Cfrac%7Bm%7D%7Bn%7D+%3D+%5Cfrac%7Bn+%5Ctimes+%28m+%2B+n%29+%2B+m+%5Ctimes+%28m+-+n%29%7D%7Bn+%5Ctimes+%28m+-+n%29%7D+%3D+%5Cfrac%7Bmn+%2B+%7Bn%7D%5E%7B2%7D+%2B+%7Bm%7D%5E%7B2%7D+-+mn+%7D%7Bmn+-+%7Bn%7D%5E%7B2%7D+%7D+%3D+%5Cfrac%7B+%7Bn%7D%5E%7B2%7D+%2B+%7Bm%7D%5E%7B2%7D+%7D%7Bmn+-+%7Bn%7D%5E%7B2%7D+%7D+)
3)
![\frac{3 {x}^{2} }{ {x}^{2} - 1} - \frac{3x}{x - 1} = \frac{3 {x}^{2} }{(x - 1)(x + 1)} - \frac{3x}{x - 1} = \frac{3 {x}^{2} - 3x(x + 1) }{(x - 1)(x + 1)} = \frac{3 {x}^{2} - 3 {x}^{2} - 3x }{ {x}^{2}1 } = \frac{ - 3x}{ {x}^{2}1 } = - \frac{3x}{ {x}^{2} - 1}](https://tex.z-dn.net/?f=+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+%7D%7B+%7Bx%7D%5E%7B2%7D+-+1%7D+-+%5Cfrac%7B3x%7D%7Bx+-+1%7D+%3D+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+%7D%7B%28x+-+1%29%28x+%2B+1%29%7D+-+%5Cfrac%7B3x%7D%7Bx+-+1%7D+%3D+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+-+3x%28x+%2B+1%29+%7D%7B%28x+-+1%29%28x+%2B+1%29%7D+%3D+%5Cfrac%7B3+%7Bx%7D%5E%7B2%7D+-+3+%7Bx%7D%5E%7B2%7D+-+3x+%7D%7B+%7Bx%7D%5E%7B2%7D1+%7D+%3D+%5Cfrac%7B+-+3x%7D%7B+%7Bx%7D%5E%7B2%7D1+%7D+%3D+-+%5Cfrac%7B3x%7D%7B+%7Bx%7D%5E%7B2%7D+-+1%7D+)
4)
![\frac{2 {y}^{2} }{y - 8} - 2y = \frac{2 {y}^{2} - 2y(y - 8)}{y - 8} = \frac{2 {y}^{2} - 2 {y}^{2} + 16y}{y - 8} = \frac{16y}{y - 8}](https://tex.z-dn.net/?f=+%5Cfrac%7B2+%7By%7D%5E%7B2%7D+%7D%7By+-+8%7D+-+2y+%3D+%5Cfrac%7B2+%7By%7D%5E%7B2%7D+-+2y%28y+-+8%29%7D%7By+-+8%7D+%3D+%5Cfrac%7B2+%7By%7D%5E%7B2%7D+-+2+%7By%7D%5E%7B2%7D+%2B+16y%7D%7By+-+8%7D+%3D+%5Cfrac%7B16y%7D%7By+-+8%7D+)
#3
![(3a - {a}^{2} ) ^{2} - {a}^{2} (a - 2)(a + 2) + 2a(7 + 3 {a}^{2} ) = 9 {a}^{2} - 6 {a}^{3} + {a}^{4} - {a}^{2} ( {a}^{2} - 4) + 14a + 16 {a}^{3} = 9 {a}^{2} - 6 {a}^{3} + {a}^{4} - {a}^{4} + 4 {a}^{2} + 14a + 6 {a}^{3} = 13 {a}^{2} + 14a](https://tex.z-dn.net/?f=%283a+-+%7Ba%7D%5E%7B2%7D+%29+%5E%7B2%7D+-+%7Ba%7D%5E%7B2%7D+%28a+-+2%29%28a+%2B+2%29+%2B+2a%287+%2B+3+%7Ba%7D%5E%7B2%7D+%29+%3D+9+%7Ba%7D%5E%7B2%7D+-+6+%7Ba%7D%5E%7B3%7D+%2B+%7Ba%7D%5E%7B4%7D+-+%7Ba%7D%5E%7B2%7D+%28+%7Ba%7D%5E%7B2%7D+-+4%29+%2B+14a+%2B+16+%7Ba%7D%5E%7B3%7D+%3D+9+%7Ba%7D%5E%7B2%7D+-+6+%7Ba%7D%5E%7B3%7D+%2B+%7Ba%7D%5E%7B4%7D+-+%7Ba%7D%5E%7B4%7D+%2B+4+%7Ba%7D%5E%7B2%7D+%2B+14a+%2B+6+%7Ba%7D%5E%7B3%7D+%3D+13+%7Ba%7D%5E%7B2%7D+%2B+14a)
p.s. В последнем примере нужно листать в лево. Пример вышел очень большим.
D=b^2-4ac=(-7)^2-4*1*12=49-48=1,D больше 0,значит,2 д.к
х1,2= -b+-√D/2а
х1= 4-1/2,х2=4+1/2
х1=3/2,х2=5/2
х1=1,5,х2=2,5
Разность в 2,5-1,5=1 раз
пусть скорость катера х. скорость по течению х+2, протв течения х-2.Составляем уравнение
40/(х+2) + 6/(х-2)= 3
40(х-2)+6(х+2)-3(х+2)(х-2)=0
-3х^2 +46х -56=0
х1=14
х2=8/6(слишком маленькая для катера)
Значит ответ 14.