\(\frac{2x+2}{5x-3}=\frac{2x+12}{5x+18}\)

\(\Rightarrow\left(2x+2\right)\left(5x+18\right)=\left(2x+12\right)\left(5x-3\right)\)

\(\Rightarrow\left(2x+2\right)5x+\left(2x+2\right)18=\left(2x+12\right)5x-\left(2x+12\right)3\)

\(\Rightarrow10x^2+10x+36x+36=10x^2+60x-6x-36\)

\(\Rightarrow46x+36=54x-36\)

\(\Rightarrow54x-46x=36+36\)

\(\Rightarrow8x=72\)

\(\Rightarrow x=9\)

Vậy \(x=9\)

Áp dụng t/c dãy tỉ số bằng nhau, ta có:

\(\frac{2x+2}{5x-3}=\frac{2x+12}{5x+18}=\frac{\left(2x+12\right)-\left(2x+2\right)}{\left(5x+18\right)-\left(5x-3\right)}=\frac{10}{21}\)

Có: \(\frac{2x+2}{5x-3}=\frac{10}{21}\)

<=> 21(2x+2) = 10(5x-3)

<=> 42x+42 = 50x-30

<=> 8x = 72

<=> x = 9

\(\frac{2x+2}{5x-3}=\frac{2x+12}{5x+18}\)

\(\Rightarrow\left(2x+2\right)\left(5x+18\right)=\left(5x-3\right)\left(2x+12\right)\)

\(\Rightarrow2x\left(5x+18\right)+2\left(5x+18\right)=5x\left(2x+12\right)-3\left(2x+12\right)\)

\(\Rightarrow10x^2+36x+10x+36=10x^2+60x-6x-36\)

\(\Rightarrow46x+36=54x-36\)

\(\Rightarrow36+36=54x-46x\)

\(\Rightarrow72=8x\)

\(\Rightarrow x=9\)

tck cho to nha 

2x(5x+18)+2(5x+18)=5x(2x+12)+3(3x-1)

10x^2+2x+10x+2=10x+-5x+9x-3

=> 10x^2+2x+10x-10x^2+5x-9x=-3-2

-2X=-5

x=5/2

x=5/2

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:\(\frac{2x+3}{5x+2}=\frac{4x+5}{10x+2}=\frac{2\left(2x+3\right)-\left(4x+5\right)}{2\left(5x+2\right)-\left(10x+2\right)}=\frac{1}{2}\)
=> \(\frac{2x+3}{5x+2}=\frac{1}{2}\) => 2(2x+3) = 5x+ 2 => 4x + 6 = 5x + 2 => 6 - 2 = 5x - 4x => 4 = x

Vậy x = 4