\(1,\dfrac{3x+2}{6}-\dfrac{3x-2}{4}=\dfrac{15}{8}\\ \Leftrightarrow\dfrac{4\left(3x+2\right)}{24}-\dfrac{6\left(3x-2\right)}{24}-\dfrac{45}{24}=0\\ \Leftrightarrow12x+24-18x+12-45=0\\ \Leftrightarrow-6x-9=0\\ \Leftrightarrow x=-\dfrac{3}{2}\)

2, ĐKXĐ:\(x\ne\pm3\)

\(\dfrac{x+2}{3+x}-\dfrac{x}{3-x}=\dfrac{8x-6}{9-x^2}\\ \Leftrightarrow\dfrac{\left(x+2\right)\left(3-x\right)}{\left(3+x\right)\left(3-x\right)}-\dfrac{x\left(3+x\right)}{\left(3+x\right)\left(3-x\right)}-\dfrac{8x-6}{\left(3+x\right)\left(3-x\right)}=0\\ \Leftrightarrow\dfrac{-x^2+x+6-3x-x^2-8x+6}{\left(3+x\right)\left(3-x\right)}=0\\ \Leftrightarrow-2x^2-10x+12=0\\ \Leftrightarrow x^2+5x-6=0\\ \Leftrightarrow\left(x-1\right)\left(x+6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=1\left(tm\right)\\x=-6\left(tm\right)\end{matrix}\right.\)

\(a,\dfrac{3x+2}{6}-\dfrac{3x-2}{4}=\dfrac{15}{8}\)

\(\Leftrightarrow4\left(3x+2\right)-6\left(3x-2\right)=45\)

\(\Leftrightarrow12x+8-18x+12=45\)

\(\Leftrightarrow12x-18x=45-12-8\)

\(\Leftrightarrow-6x=25\)

\(\Leftrightarrow x=\dfrac{-25}{6}\)

Vậy \(S=\left\{\dfrac{-25}{6}\right\}\)

\(b,\dfrac{x+2}{3+x}-\dfrac{x}{3-x}=\dfrac{8x-6}{9-x^2}\left(ĐKXĐ:x\ne3;x\ne-3\right)\)

\(\Leftrightarrow\left(x+2\right)\left(3-x\right)-x\left(3+x\right)=8x-6\)

\(\Leftrightarrow3x-x^2+6-2x-3x-x^2=8x-6\)

\(\Leftrightarrow-x^2-x^2+3x-2x-3x-8x=-6+6\)

\(\Leftrightarrow-2x^2-10x=0\)

\(\Leftrightarrow-2x\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}-2x=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(nhận\right)\\x=5\left(nhận\right)\end{matrix}\right.\)

Vậy \(S=\left\{0;5\right\}\)

Tính phải k nhỉ?

`1)`

`2x + 3x + 5x`

`= (2 + 3 + 5)x`

`= 10x`

`2)`

`2.x - x + 3.x`

`= (2 - 1 + 3)x`

`= 4x`

`3)`

`9.x - 3 - 3.x`

`= (9 - 3)x - 3`

`= 6x - 3`

`4)`

Thiếu dấu, bạn bổ sung thêm

`5)`

`x - 0,2x - 0,1x`

`= (1 - 0,2 - 0,1)x`

`=0,7x`

`6)`

\(\dfrac{7}{2}x-\dfrac{1}{2}x=\left(\dfrac{7}{2}-\dfrac{1}{2}\right)x=3x\)

a) 2/3 + 11/3 = 13/3

b) 4/5 - 2/3 = 12/15 - 10/15 = 2/15

c) 21/9 x 3/4 = 7/3 x 3/4 = 21/12 = 7/4

d) 6/5 : 6/9 = 6/5 x 9/6 = 54/30 = 9/5

chúc bạn học tốt!

\(A=4\sqrt{x}-\frac{\left(\sqrt{x}+3\right)^2\left(\sqrt{x}-3\right)}{\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)}\)

\(=4\sqrt{x}-\left(\sqrt{x}+3\right)\)

\(=3\sqrt{x}-3\)

\(B=\frac{\sqrt{\left(3x+2\right)^2}}{3x+2}=\frac{|3x+2|}{3x+2}\)

\(TH1:3x+2>0\Rightarrow B=1\)

\(TH2:3x+2< 0\Rightarrow B=-1\)

A <=> 4√x - [ ( (√x )^2 + 2√x3+ 3^2)*( √x -3)]/ (x-9)

<=> 4√x - [(√x+3)^2×(√x-3)]/( x-9)

<=> 4√x - [(√x+3)*(x-9)]/(x-9)

<=> 4√x - √x -3

<=> 3√x -3

b, <=> √[(3*x) ^2+2*3x*2+2^2]/(3x+2)

<=> √[( 3x+2)^2] /(3x+2) 

<=> (3x+2)/(3x+2) = 1

1) (x - 35) - 120 = 0

x - 35 = 120

x = 120 + 35

x = 155

2) 310 - (118 - x) = 217

118 - x = 310 - 217

118 - x = 93

x = 118 - 93

x = 25

3) 156 - (x + 61) = 82

x + 61 = 156 - 82

x + 61 = 74

x = 74 - 61

x = 13

4) 814 - (x - 305) = 712

x - 305 = 814 - 712

x - 305 = 102

x = 102 + 305 = 407

5) 100 - 7 - (x - 5) = 58

x - 5 = 93 - 58

x - 5 = 35

x = 35 + 5 = 40

6) 12(x - 1) : 3 = 4³ + 2³

4(x - 1) = 72

x - 1 = 18

x = 18 + 1 = 19

7) 24 + 5x = 7⁵ : 7³

24 + 5x = 49

5x = 25

x = 25 : 5 = 5

8) 5(x - 1) : 3 = 4³ + 2³

\(\dfrac{5}{3}\left(x-1\right)=72\)

x - 1 = \(\dfrac{216}{5}\)

x = 221/5

9) 5(x - 4)² - 7 = 13

5(x - 4)² = 20

(x - 4)² = 4

\(\Rightarrow\left[{}\begin{matrix}x-4=2\\x-4=-2\end{matrix}\right.\)   \(\Rightarrow\left[{}\begin{matrix}x=6\\x=2\end{matrix}\right.\)

10) (x + 1) + (x + 2) + ... + (x + 30) = 795

=> (x + x + x + ... + x) + (1 + 2 + 3 +...+ 30) = 795 (1)

Đặt A = 1 + 2 + 3 +...+ 30

Số số hạng trong A là: (30 - 1) : 1 + 1 = 30 (số)

Tổng A bằng : (30 + 1).30 : 2 =465

Thay A = 465 vào (1) , ta được:

30x + 465 = 795

=> 30x =330

=> x =11

1: =>x-35=120

=>x=120+35=155

2: =>118-x=310-217=93

=>x=118-93=25

3: =>x+61=156-82=74

=>x=74-61=13

4: =>x-305=814-712=102

=>x=102+305=407

5: =>93-(x-5)=58

=>x-5=35

=>x=40

6: =>4(x-1)=64+8=72

=>x-1=18

=>x=19

7: =>5x+24=49

=>5x=25

=>x=5

8: =>5(x-1):3=4^3+2^3=64+8=72

=>5(x-1)=216

=>x-1=216/5

=>x=221/5

x - 4/5 = 3/7

x = 3/7 + 4/5

x = 43/35

x + 3/7 = 4/5

x = 4/5 - 3/7

x = 13/35

19/20 - x = 8/5 - 3/4

19/20 - x =  17/20

x = 19/20 - 17/20

x = 2/20 = 1/10

4/5 x X = 6/9 - 4/7

4/5 x X = 2/21

x = 2/21 : 4/5

x =5/42

x : 7/9 = 6/8

x = 6/8 x 7/9

x = 7/12

2/3 - x/6 = 6/18

x/6 = 2/3 - 6/18

x/6 = 1/3

x/6 = 2/6

=> x =2

1. x = 43/35

2. x = 13/35

3. x = 1/10

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