Đáp án:

\(1)\ x=\dfrac{23}7\\ 2)\ x=\dfrac{-2}3\\ 3)\ x=-23\\ 4)\ x=7\\ 5)\ x=\dfrac85\\ 6)\ x=\dfrac{21}4\\ 7)\ x=\dfrac{-4}5\)

Giải thích các bước giải:

\(1)\ \dfrac3{x-1}=\dfrac{21}{16}\\ ⇔21(x-1)=3.16\\ ⇔x-1=\dfrac{3.16}{21}\\ ⇔x-1=\dfrac{16}{7}\\ ⇔x=\dfrac{23}{7}\\ \text{Vậy x = $\dfrac{23}{7}$}\\ 2)\ \dfrac{1,2}{30}=\dfrac{3x+4}{50}\\ ⇔30(3x+4)=1,2.50\\ ⇔30(3x+4)=60\\ ⇔3x+4=2\\ ⇔3x=-2\\ ⇔x=\dfrac{-2}3\\ \text{Vậy x = $\dfrac{-2}3$}\\ 3)\ \dfrac{x-1}{x-5}=\dfrac67\\ ⇔7(x-1)=6(x-5)\\ ⇔7x-7=6x-30\\ ⇔7x-6x=-30+7\\ ⇔x=-23\\ \text{Vậy x = (- 23)}\\ 4)\ \dfrac{x-1}3=\dfrac{x+3}5\\ ⇔5(x-1)=3(x+3)\\ ⇔5x-5=3x+9\\ ⇔5x-3x=9+5\\ ⇔2x=14\\ ⇔x=7\\ \text{Vậy x = 7}\\ 5)\ \dfrac{3}7=\dfrac{2x+1}{3x+5}\\ ⇔3(3x+5)=7(2x+1)\\ ⇔9x+15=14x+7\\ ⇔9x-14x=7-15\\ ⇔-5x=-8\\ ⇔x=\dfrac{-8}{5}=\dfrac85\\ \text{Vậy x = $\dfrac85$}\\ 6)\ \dfrac{2x+3}{6}=\dfrac{7x-3}{15}\\ ⇔15(2x+3)=6(7x-3)\\ ⇔30x+45=42x-18\\ ⇔30x-42x=-18-45\\ ⇔-12x=-63\\ ⇔x=\dfrac{-63}{-12}=\dfrac{21}4\\ \text{Vậy x = $\dfrac{21}4$}\\ 7)\ \dfrac{6x-5}{-7}=\dfrac{5x-3}{-5}\\ ⇔-5(6x-5)=-7(5x-3)\\ ⇔-30x+25=-35x+21\\ ⇔-30x+35x=21-25\\ ⇔5x=-4\\ ⇔x=\dfrac{-4}5\\ \text{Vậy x = $\dfrac{-4}5$}\)

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Giải thích các bước giải:

1. `3/(x-1) = 21/16`

`⇔ 16 . 3 = 21(x-1)`

`⇔ 48 = 21x - 21`

`⇔ 21x = 69 ⇔ x = 23/7`

Vậy `x=23/7`

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2. `(1,2)/30 = (3x+4)/50`

`⇔ 3x + 4 = (1,2)/30 . 50`

`⇔ 3x + 4 = 2`

`⇔ 3x = -2`

`⇔ x = -2/3`

Vậy `x=(-2)/3`

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3. `(x-1)/(x-5) = 6/7`

`⇔ 7(x-1) = 6(x-5)`

`⇔ 7x - 7 = 6x - 30`

`⇔ x = -23`

Vậy `x=-23`

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4. `(x-1)/3 = (x+3)/5`

`⇔ 5(x-1) = 3(x+3)`

`⇔ 5x - 5 = 3x + 9`

`⇔ 2x = 14`

`⇔ x=7`

Vậy `x=7`

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5. `3/7 =(2x+1)/(3x + 5)`

`⇔ 3(3x + 5) = 7(2x + 1)`

`⇔ 9x + 15 = 14x + 7`

`⇔ -5x = -8`

`⇔ x = 8/5`

Vậy `x=8/5`

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6. `(2x + 3)/6 = (7x  - 3)/15`

`⇔ 15(2x + 3) = 6(7x-3)`

`⇔ 30x + 45 = 42x - 18`

`⇔ -12x = -63`

`⇔ x=21/4`

Vậy `x=21/4`

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7. `(6x - 5)/-7 = (5x - 3)/-5`

`⇔ -7(5x - 3) = -5(6x - 5)`

`⇔ -35x + 21 = -30x + 25`

`⇔ -5x = 4`

`⇔ x = -4/5`

Vậy `x=-4/5`

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