\(\dfrac{x+1}{65}+\dfrac{x+3}{63}+\dfrac{x+5}{61}+\dfrac{x+7}{59}\)

\(\Leftrightarrow\dfrac{x+1}{65}+\dfrac{x+3}{63}-\dfrac{x+5}{61}-\dfrac{x+7}{59}=0\)

\(\left(\dfrac{x+1}{65}+1\right)+\left(\dfrac{x+3}{63}+1\right)-\left(\dfrac{x+5}{61}+1\right)-\left(\dfrac{x+7}{59}+1\right)\)

\(\Leftrightarrow\dfrac{x+66}{65}+\dfrac{x+66}{63}+\dfrac{x+66}{61}+\dfrac{x+66}{59}=0\)

\(\Leftrightarrow\left(x+66\right).\left[\left(\dfrac{1}{65}+\dfrac{1}{63}\right)-\left(\dfrac{1}{61}+\dfrac{1}{59}\right)\right]\)\(=0\)

Do \(\dfrac{1}{65}< \dfrac{1}{63}< \dfrac{1}{61}< \dfrac{1}{59}\) 

\(\Rightarrow\left(\dfrac{1}{65}+\dfrac{1}{63}\right)-\left(\dfrac{1}{61}+\dfrac{1}{59}\right)< 0\)

Vậy để \(\left(x+66\right).\left[\left(\dfrac{1}{65}+\dfrac{1}{63}\right)-\left(\dfrac{1}{61}+\dfrac{1}{59}\right)\right]=0\)

\(\Leftrightarrow x+66=0\)

\(\Leftrightarrow x=-66\)

Vậy \(x\in\left\{-66\right\}\)

mỗi phân số cộng thêm 1 ta có

\(\frac{x+66}{65}+\frac{x+66}{63}=\frac{x+66}{61}+\frac{x+66}{59}\)

rồi đặt x+66 làm thừa số chung sau đó giải tiếp

x thuộc tập hợp rỗng

\(\frac{x-1}{65}+\frac{x-3}{63}=\frac{x-5}{61}+\frac{x-7}{59}\)

\(\Rightarrow\frac{x-1}{61}-1\frac{x-3}{63}+-1=\frac{x-5}{61}-1+\frac{x-7}{59}-1\)

\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)

\(\Rightarrow\left(x-66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)

\(\Rightarrow x=66\)

\(\Leftrightarrow x+66=0\)

hay x=-66

\(\dfrac{x+1}{65}+\dfrac{x+3}{63}=\dfrac{x+5}{61}+\dfrac{x+7}{59}\\ \Rightarrow\left(\dfrac{x+1}{65}+1\right)+\left(\dfrac{x+3}{63}+1\right)=\left(\dfrac{x+5}{61}+1\right)+\left(\dfrac{x+7}{59}+1\right)\\ \Rightarrow\dfrac{x+66}{65}+\dfrac{x+66}{63}-\dfrac{x+66}{61}-\dfrac{x+66}{59}=0\\ \Rightarrow\left(x+66\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\right)=0\\ \Rightarrow x+66=0\\ \Rightarrow x=-66\)

\(\dfrac{x+1}{65}+\dfrac{x+3}{63}=\dfrac{x+5}{61}+\dfrac{x+7}{59}\\ \dfrac{x+66}{65}+\dfrac{x+66}{63}-\dfrac{x+66}{61}-\dfrac{x+66}{59}=0\\ \left(x+66\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\right)=0\\ x+66=0\\ x=-66\)

(x - 1)/65 + (x - 3)/63 = (x - 5)/61 + (x - 7)/59

tương tự:

(x - 1)/65 - 1 + (x - 3)/63 - 1 = (x - 5)/61 - 1 + (x - 7)/59 - 1

Rút gọn được:

(x - 66) x (1/65 + 1/63) = (x - 66) x (1/61 + 1/59)

(x - 66) x (1/65 + 1/63 - 1/61 - 1/59) = 0

\(\Rightarrow\) x = 66

Mỗi phần cộng thêm số 1 ta có:

\(\frac{x+66}{65}+\frac{x+66}{63}=\frac{x+66}{61}+\frac{x+66}{59}\)

Rồi đặt x + 66 làm thừa số chung.

giải pt : (x + 1)/65 + (x + 3)/63 = (x + 5)/61 + (x + 7)/59 
<==> (x + 1)/65 + 1 + (x + 3)/63 + 1 = (x + 5)/61 + 1 + (x + 7)/59 + 1 
<==> (x + 66)/65 + (x + 66)/63 = (x + 66)/61 + (x + 66)/59 
<==> (x + 66) = 0 
==> x = -66

\(\dfrac{x-1}{65}+\dfrac{x-3}{63}=\dfrac{x-5}{61}+\dfrac{x-7}{59}\)

\(\Leftrightarrow\dfrac{x-1}{65}-1+\dfrac{x-3}{63}-1=\dfrac{x-5}{61}-1+\dfrac{x-7}{59}-1\)

\(\Leftrightarrow\dfrac{x-66}{65}+\dfrac{x-66}{63}=\dfrac{x-66}{61}+\dfrac{x-66}{59}\)

\(\Leftrightarrow\left(x-66\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\right)=0\)

\(\Leftrightarrow x-66=0\)

\(\Leftrightarrow x=66\)

Vậy x=66.