Đáp án + Giải thích các bước giải:
Bài 1 :
`3/5 - 7/3 + (-2)/15 = 9/15 - 35/15+(-2)/15=(9-35-2)/15=-28/15`
`(-7/12)*5/14 + 9/14*(-7/12) - (-3)/4 = (-7/12)(5/14+9/14)-(-3)/4` $\\$ `= (-7/12)*1-(-9)/12=(-7/12)-(-9)/12=(-7/12)+9/12=2/12=1/6`
`(-3/2)^3 + (-49)/24*3/14 - (5/8-27/8)` $\\$ `= -27/8+(-7)/8*1/2-5/8+27/8` $\\$ `= -27/8 + (-7)/16 - 5/8 + 27/8 = (-7)/16 - 5/8` $\\$ `= (-7)/16 - 10/16 = -17/16`
Bài 2 :
`x - 5/3 = -2 => x - 5/3 = -6/3` $\\$ `=> x = -6/3+5/3=-1/3`
Vậy `x = -1/3`
`(x - (-5)/9) : 5/3 = -7/15` $\\$ `=> (x - (-5)/9) = -7/15*5/3=-7/3*1/3=-7/9` $\\$ `=> x + 5/9= -7/9 => x = -12/9=-4/3`
Vậy `x = -4/3`
`(x + 5)/4 = (x - 3)/5 => 5(x + 5) = 4(x - 3)` $\\$ `=> 5x + 25 = 4x - 12 => 5x - 4x = -12 - 25` $\\$ `=> x = -37`
Bài 3 :
`1 + 1/5 + 3/35+...+3/9603 + 3/9999` $\\$ `= 1 + (3/15 + 3/35 + ... + 3/9603 + 3/9999)` $\\$ `= 1 + (3/(3*5) + 3/(5*7) + ... + 3/(97*99) + 3/(99*101))` $\\$ `= 1 + [3/2(2/(3*5) + 2/(5*7) + ... + 2/(97*99) + 2/(99*101))]` $\\$ `= 1 + [3/2(1/3 - 1/5 + ... + 1/99 - 1/101)]` $\\$ `= 1 + [3/2(1/3 - 1/101)]` $\\$ `= 1 + 3/2*98/303 = 1 + 49/101` $\\$ `= 101/101 + 49/101 = 150/101`
