Câu a:

\(\frac{x+5}{x+9}\) = \(\frac{x+4}{x+3}\)

(\(x\) + 5)(\(x+3\)) = (\(x+4\))(\(x+9\))

\(x^2\) + 3\(x\) + 5\(x\) + 15 = \(x^2\) + 9\(x\) + 4\(x\) + 36

\(x^2+3x+5x\) - \(x^2-9x\) - 4\(x\) = 36 - 15

(\(x^2-x^2\)) + (\(3x+5x\) - 9\(x-4x\)) = 21

0 + (8\(x\) - 9\(x\) - 4\(x\)) = 21

-\(x-4x\) = 21

-5\(x\) = 21

\(x\) = 21 : (-5)

\(x\) = - \(\frac{21}{5}\)

Vậy \(x=-\frac{21}{5}\)

x=3

x=1

x=4

mk cần bài giải cụ thể nhé

a: x+2x+3x+...+2011x=2012*2013

=>\(x\left(1+2+\cdots+2011\right)=2012\cdot2013\)

=>\(x\cdot2011\cdot\frac{2012}{2}=2012\cdot2013\)

=>\(x=\frac{2012\cdot2013}{2011\cdot1006}=\frac{2\cdot2013}{2011}=\frac{4026}{2011}\)

b: Đặt A=1+3+5+...+99

Số số hạng trong dãy số là:

\(\frac{99-1}{2}+1=\frac{98}{2}+1=49+1=50\) (số)

Tổng của dãy số là:

\(A=\left(99+1\right)\cdot\frac{50}{2}=50\cdot50=2500\)

Ta có: \(1+3+5+\cdots+99=\left(x+1\right)^2\)

=>\(\left(x+1\right)^2=2500\)

=>\(\left[\begin{array}{l}x+1=50\\ x+1=-50\end{array}\right.\Rightarrow\left[\begin{array}{l}x=49\\ x=-51\end{array}\right.\)

c:

Đặt B=1+3+5+...+199

Số số hạng của dãy là:

\(\frac{199-1}{2}+1=\frac{198}{2}+1=99+1=100\) (số)

Tổng của dãy số là:

\(B=\left(199+1\right)\cdot\frac{100}{2}=100^2\)

(x+1)+(2x+3)+(3x+5)+...+(100x+199)=30200

=>(x+2x+3x+...+100x)+(1+3+5+...+199)=30200

=>\(x\left(1+2+\cdots+100\right)+\left(1+3+\cdots+199\right)=30200\)

=>\(x\cdot100\cdot\frac{101}{2}+10000=30200\)

=>\(x\cdot5050=20200\)

=>x=4

Mik cảm ơn bạn.

\(-5.\left(x+\frac{1}{5}\right)-\frac{1}{2}.\left(x-\frac{2}{3}\right)=\frac{3}{2}x-\frac{5}{6}\)

\(\Rightarrow-5x-1-\frac{1}{2}x+\frac{1}{3}=\frac{3}{2}x-\frac{5}{6}\)

\(\Rightarrow-5x-\frac{1}{2}x-\frac{3}{2}x=\frac{-5}{6}-\frac{1}{3}+1\)

\(\Rightarrow-7x=\frac{-1}{6}\)

\(\Rightarrow x=\frac{1}{42}\)

Vậy ...

\(\)

\(3.\left(3x-\frac{1}{2}\right)^3+\frac{1}{9}=0\)

\(\Rightarrow3.\left(3x-\frac{1}{2}\right)^3=\frac{-1}{9}\)

\(\Rightarrow\left(3x-\frac{1}{2}\right)^3=\frac{-1}{27}\)

\(\Rightarrow\left(3x-\frac{1}{2}\right)^3=\left(\frac{-1}{3}\right)^3\)

\(\Rightarrow3x-\frac{1}{2}=\frac{-1}{3}\)

\(\Rightarrow3x=\frac{1}{6}\)

\(\Rightarrow x=\frac{1}{18}\)

Vậy...

làm luông di

a: \(\Leftrightarrow6x+10⋮2x+1\)

\(\Leftrightarrow6x+3+7⋮2x+1\)

\(\Leftrightarrow2x+1\in\left\{1;-1;7;-7\right\}\)

hay \(x\in\left\{0;-2;3;-4\right\}\)

b: \(\Leftrightarrow6x+2⋮2x-1\)

\(\Leftrightarrow6x-3+5⋮2x-1\)

\(\Leftrightarrow2x-1\in\left\{1;-1;5;-5\right\}\)

hay \(x\in\left\{1;0;3;-2\right\}\)

1: Để A nguyên thì 2x+2+3 chia hết cho x+1

=>3 chia hết cho x+1

mà x+1>=1

nên \(x+1\in\left\{1;3\right\}\)

=>\(x\in\left\{0;2\right\}\)

2: Để B nguyên thì 2x+4 chia hết cho x

=>4 chia hết cho x

=>\(x\in\left\{1;2;4\right\}\)

3: Để C nguyên thì 2x+2+5 chia hết cho x+1

=>5 chia hết cho x+1

mà x+1>=1

nên \(x+1\in\left\{1;5\right\}\)

=>\(x\in\left\{0;4\right\}\)

4: Để D nguyên thì 3x-3+8 chia hết cho x-1

=>8 chia hết cho x-1

=>\(x-1\in\left\{-1;1;2;4;8\right\}\)

hay \(x\in\left\{0;2;3;5;9\right\}\)

5: Để E nguyên thì 3x-3+9 chia hết cho x-1

=>\(x-1\in\left\{-1;1;3;9\right\}\)

hay \(x\in\left\{0;2;4;10\right\}\)

a) \(\frac{3x}{5}=\frac{1-4x}{3}\)

=> 3x . 3 = 5.(1-4x)

=>  9x    =     5 -20x

=> 9x + 20x =5

=> 29x        =5

=> x =\(\frac{5}{29}\)

b)\(\frac{x}{5}=\frac{15}{3x}\)

=>3x . x = 15 . 5

=> \(3x^2\)=75

=>  \(x^2\)=25

=> x       = \(\sqrt{25}\)

=>x         = 5                 CHÚC BẠN HỌC TỐT 

a)\(\frac{3x}{5}=\frac{1-4x}{3}\)

=>3x.3=5(1-4x)

=>9x=5-20x

=>9x+20x=5

=>29x=5

=>x=5/29

VẬy,...

Câu a:

- \(\frac12\)(3 - 2\(x\)) - 7 = 5 - \(\frac13\)(\(x\) - \(\frac45\))

- \(\frac32\) + \(x\) - 7 = 5 - \(\frac13x\) + \(\frac{4}{15}\)

\(x\) + \(\frac13x\) = 5 + \(\frac{4}{15}\) + 7 + \(\frac32\)

(1 + \(\frac13\))\(x\) = \(\frac{150}{30}\) + \(\frac{8}{30}\) + \(\frac{210}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{158}{30}\) + \(\frac{210}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{368}{30}\) + \(\frac{45}{30}\)

\(\frac43x\) = \(\frac{413}{30}\)

\(x\) = \(\frac{413}{30}\) : \(\frac43\)

\(x\) = \(\frac{413}{40}\)

Vậy \(x=\frac{413}{40}\)

Câu b:

(5 - 3x/2) : - 1 3/8 = - 7 1/3

(5 - 3x/2) : (-11/8) = - 22/3

5 - 3x/2 = - 22/3 x (-11/8)

5 - 3x/2 = 121/12

3x/2 = 5 - 121/12

3x/2 = - 61/12

x = - 61/12 : 3/2

x = -61/18

Vậy x = - 61/18