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![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{x+1}{65}+\dfrac{x+3}{63}+\dfrac{x+5}{61}+\dfrac{x+7}{59}\)
\(\Leftrightarrow\dfrac{x+1}{65}+\dfrac{x+3}{63}-\dfrac{x+5}{61}-\dfrac{x+7}{59}=0\)
\(\left(\dfrac{x+1}{65}+1\right)+\left(\dfrac{x+3}{63}+1\right)-\left(\dfrac{x+5}{61}+1\right)-\left(\dfrac{x+7}{59}+1\right)\)
\(\Leftrightarrow\dfrac{x+66}{65}+\dfrac{x+66}{63}+\dfrac{x+66}{61}+\dfrac{x+66}{59}=0\)
\(\Leftrightarrow\left(x+66\right).\left[\left(\dfrac{1}{65}+\dfrac{1}{63}\right)-\left(\dfrac{1}{61}+\dfrac{1}{59}\right)\right]\)\(=0\)
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 \(x\in\left\{-66\right\}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
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
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x-1}{65}+\frac{x-3}{63}=\frac{x-5}{61}+\frac{x-7}{59}\)
\(\Rightarrow\frac{x-1}{61}-1\frac{x-3}{63}+-1=\frac{x-5}{61}-1+\frac{x-7}{59}-1\)
\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
\(\Rightarrow\left(x-66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
\(\Rightarrow x=66\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Rightarrow\frac{x-1}{65}-1+\frac{x-3}{63}-1=\frac{x-5}{61}-1+\frac{x-7}{59}-1\)
\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}-\frac{x-66}{61}-\frac{x-66}{59}=0\)
\(\Rightarrow x-66=0\).Do\(\frac{x-66}{65}+\frac{x-66}{63}-\frac{x-66}{61}-\frac{x-66}{59}\ne0\)
\(\Rightarrow x=66\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\)
\(\Leftrightarrow\frac{\left(x+1\right)}{65}-1+\frac{\left(x+3\right)}{63}-1=\frac{\left(x+5\right)}{61}-1+\frac{\left(x+7\right)}{59}\)
\(\Leftrightarrow\left(x-66\right).\left(\frac{1}{65}+\frac{1}{63}\right)=\left(x-66\right).\left(\frac{1}{61}+\frac{1}{59}\right)\)
\(\Leftrightarrow\left(x-66\right).\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
\(\Rightarrow x=66\)
\(\frac{x+1}{65}+\frac{x+3}{63}=\frac{x+5}{61}+\frac{x+7}{59}\)
=> \(\left(\frac{x+1}{65}+1\right)+\left(\frac{x+3}{63}+1\right)=\left(\frac{x+5}{61}+1\right)+\left(\frac{x+7}{59}+1\right)\)
=> \(\frac{x+66}{65}+\frac{x+66}{63}=\frac{x+66}{61}+\frac{x+66}{59}\)
=> \(\left(x+66\right).\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
=> x + 66 = 0
=> x = 0 - 66
=> x = -66
(x-100)/24 + (x-98)/26 + (x-96)/28 = 3![http://xxkanonxx.deviantart.com/art/Fanart-Hotarumaru-Touken-Ranbu-545295951 Kết quả hình ảnh](data:image/jpeg;base64,/9j/4AAQSkZJRgABAQAAAQABAAD/2wCEAAkGBwgHBgkIBwgKCgkLDRYPDQwMDRsUFRAWIB0iIiAdHx8kKDQsJCYxJx8fLT0tMTU3Ojo6Iys/RD84QzQ5OjcBCgoKDQwNGg8PGjclHyU3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3Nzc3N//AABEIAF0ARQMBIgACEQEDEQH/xAAcAAACAgMBAQAAAAAAAAAAAAAABgUHAQMECAL/xAA1EAABAwMCAwQIBQUAAAAAAAABAgMEAAURBiESMUEHE1FhFCIycYGRofAjM7HB4RVicqLR/8QAGAEBAAMBAAAAAAAAAAAAAAAAAAECAwT/xAAgEQACAgICAgMAAAAAAAAAAAAAAQIRAyESMQRBYXHw/9oADAMBAAIRAxEAPwC8aKKKAKwVADJ5V8uOIbSVOKCUpGSScAVWXaJqlq4srs9juK0rQpKpndNq4nG1A4SheCNyN/lSwWTHlx5PF6PIad4ThXdrCse/Fbs1530zYtTW5w3SyqVBWjh9WRhIeycYIzuM+I61d9mu7run0XC8ttwnkNkyUlY4WyOe9LJpok5UpiIw4/JcQ2y2MrWo4AFZjSG5LCH2VZbWApJwRkUnupk6jWzLmtrbgvLDdvhrTgrO5L7gPgASlJ8AeZ2cmW0tNobQMJSAB7hUEGyiiipAVgnFHSoXUNzXEQiNEPFKe2QOZSOWapkmoRtgV+2LUaLbpeREivATH1JSQBnhQDlWfeBj40uoiQ9N2mCq9vtwFqwtSwrL7pI3wBuQCeXLauDtH03dJlziswVocLTQLzinNkuFWcY8hj50mX+2TYMoSLpOVPlJCVF0qKyDkbHJJHQ74HhWSkslW9kp7LK1LqGz2x9iO1JckJLKW3wSSN8YPD4nFfduvTt2ENV3hLFijBKkMoRwh1fRS+hAI2HjzqnV3J6ZcnXZCyVv7ZWSd6szs11DLaiSbaeOQ1H9ZTD3rDuycEf27/DeqZOWPaNJbRZ9xkxpUOPdIiXZQjr4kCOOJaSdvZyM4zyPTNSttimJGS2XnnlElSlvHKiSc/YpQaItDjd0tOVQHlAOs5zwK8D+1OsZ5EhlDzRCm1jiSRV8OXnp9mZuoooroIMGk9Mnvbncrm4OJMRJDQ6Z5D786cDyNIcFt5+z3VppClO96nKUjcjJrk8lu4r7BFuOqcWpa1EqUSSTVS6muEqPqGW+l1bbbj/drQBjjQjGx8qsXVtwf01BakSoj+X3O7bPd59bzFVxOu00h+2uoGA+XVpkNJK0OdeYyD5Vj4WOfJzkuwiIcjvKK5EVBcaKyUKQM4zkjOOVM+j57sW9hxqQhkqZLam1tKKXAoYUgEDY9QSeYqJuYfSzBeduan+/aJ7sJ/KwfZA5YqOjQnFPkhxxLQGVLTzA8q7JtS7Lp0ehtMNPvF+I6w76JJa9ooOAroc8vsVOaPfX6I9EcOTHcIHuP85qntIahuWmZkVtm5SJsV1f48V78tAJx6vM8WMHbAq1tIOpdulzUjPCVZHlua5ccFjnFJlaG2isUV3kAeVKDDn9H1JJYdUG25QyhZ5JJ3B+eabzypG7TGzcG4FngJKrpPcKGyk47tkDLiiegxt7yKwzQbSa9AhtONStZaqXd7otD9stZU3ETgcDjoPtjoeR+nnUFfoum9Y9qCLfD79ClNKTMmxVDgW4kbDcEdMFXj8aY134ae0z/T1W1TghoDZYb9Qqb5H760vWW1Xa3sxbvarI23HfSl4NtgBShklOd+YBA8/CqQypq0Xa1ZJz+zKywpLDMe5usOrScKlALDh28MY/muG8aQkWZ3hdbQ6ypOUvIGAfEGmnXkpbkjT5ZiOuonFbY4RulRSFgEe4K+Vd0BD0a1Ox9RqSiIpP4aVqy6D5YrHJcpOL18kWK9jsENiK7e57YJjK4WGceq4vG3yJ+nlTnoSGpi2Lku+3JXxD/Ebfrmollh7UkxpltpTFqjnGM4x/1R+lPLLSWW0NtpAQkBIA6AVPj47ly9L9ZDZsooorvIMHlUHbLapV7nXeSFd8oCMyF8kNJJO3vJ+lTmKMVDQIy7WSFdEH0hsBzGA6ketj96ghp28W8Ytdx/CGwSVFOPhuKca0yX240d195QS22kqUSegrKWCEnfsFXqbuupLxHhw7o8H7TJcdkgtpQlKsqQAFp3PNXy602xNKFau8uskvq5lKc7/E7/pXH2YtNO26fc0qCnZstalnwAJwP9j86dBR4YvsGpiO1HaS0y2ltCeSUjArdRRWqVdAKKKKkBRRRQBSH2nWfVN/bh23T647MJa+OW844UqBB2G3NPXHXFPlYxQERpWwR9N2dq2xXHHUpUpanXccS1KOSTipigUUAUUUUAUUUUB//9k=)
<=> (x - 100)/24 -1 + (x-98)/26-1 (x-96)/28 -1 = 0
<=>(x-124)/24 + (x-124)/26 + (x - 124)/28 =0
<=>(x - 124) (1/24+1/26+1/28) = 0
vì 1/24+1/26+1/28 khác 0
=> x - 124 = 0
=> x = 124
2) (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).(1/65 + 1/63) = (x -66).(1/61 + 1/59)
(x - 66).(1/65 + 1/63 - 1/61 -1/59) = 0
=> x = 66 (lý luận tương tự câu trên)
a . x= 124
b.x=66