7/x + 4/5 x 9 =4 / 9x 13 +....+ 4/ 41.45 = 29/45

ĐKXĐ : `x\ne 0`

`7/x + 4/(5.9)+4/(9.13)+...+4/(41.45)=29/45`

`-> 7/x + (4/(5.9) +4/(9.13)+...+4/(41.45))=29/45`

`->7/x + (1/5-1/9+1/9-1/13+...+1/41-1/45)=29/45`

`->7/x + (1/5 -1/45)=29/45`

`-> 7/x =7/15`

`->x=15` (Tm)

Vậy `x=15`

Đáp án:

$\text{x=15}$

 Giải thích các bước giải:

$\dfrac7x+\dfrac4{5\cdot9}+\dfrac4{9\cdot13}+...+\dfrac4{41\cdot45}=\dfrac{29}{45}$

$\to\dfrac7x+\dfrac{9-5}{5\cdot9}+\dfrac{13-9}{9\cdot13}+...+\dfrac{45-41}{41\cdot45}=\dfrac{29}{45}$

$\to\dfrac7x+\dfrac15-\dfrac19+\dfrac19-\dfrac1{13}+...+\dfrac1{41}-\dfrac1{45}=\dfrac{29}{45}$

$\to\dfrac7x+\dfrac15-\dfrac1{45}=\dfrac{29}{45}$

$\to\dfrac7x+\dfrac8{45}=\dfrac{29}{45}$

$\to\dfrac7x=\dfrac{21}{45}$

$\to\dfrac7x=\dfrac7{15}$

$\text{x=15}$