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Thật tự hào khi là người Việt Nam máu đỏ, da vàng.

Quy đồng mẫu số: \(\frac{2}{9} = \frac{2}{9} , \frac{1}{3} = \frac{3}{9}\).

Nếu tử số ban đầu là \(2\)phần thì tử số mới là \(3\)phần.

Hiệu số phần bằng nhau là: 

\(3 - 2 = 1\)(phần) 

Tử số ban đầu là: 

\(6 \div 1 \times 2 = 12\)

Mẫu số là: 

\(12 \div \frac{2}{9} = 54\)

Phân số cần tìm là: \(\frac{12}{54}\).

BẠN KO ĐƯỢC NÓI TỤC NHÉ, KO LÀ CÔ HOÀI KHÓA MẬT KHẨU ĐÓ

@Đoàn Mạnh Cường

• Bất đẳng thức tam giác: |x|+|y|≥|x+y|the absolute value of x end-absolute-value plus the absolute value of y end-absolute-value is greater than or equal to the absolute value of x plus y end-absolute-value|𝑥|+|𝑦|≥|𝑥+𝑦|.
• Bất đẳng thức tam giác mở rộng: |x|+|y|+|z|≥|x+y+z|the absolute value of x end-absolute-value plus the absolute value of y end-absolute-value plus the absolute value of z end-absolute-value is greater than or equal to the absolute value of x plus y plus z end-absolute-value|𝑥|+|𝑦|+|𝑧|≥|𝑥+𝑦+𝑧|. 

1. Bước 1 . Chứng minh |a|+|b|+|c|+|a+b|+|b+c|+|c+a|≥13|5a+4b|the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of c end-absolute-value plus the absolute value of a plus b end-absolute-value plus the absolute value of b plus c end-absolute-value plus the absolute value of c plus a end-absolute-value is greater than or equal to 1 over 3 end-fraction the absolute value of 5 a plus 4 b end-absolute-value|𝑎|+|𝑏|+|𝑐|+|𝑎+𝑏|+|𝑏+𝑐|+|𝑐+𝑎|≥13|5𝑎+4𝑏|.
   • Ta có 3(|a|+|b|+|a+b|)≥|3a+3b|3 open paren the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of a plus b end-absolute-value close paren is greater than or equal to the absolute value of 3 a plus 3 b end-absolute-value3(|𝑎|+|𝑏|+|𝑎+𝑏|)≥|3𝑎+3𝑏|.
   • Ta có 3(|a|+|b|+|c|+|a+b|+|b+c|+|c+a|)≥|3a+3b+3c+3a+3b+3c|=|6a+6b+6c|3 open paren the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of c end-absolute-value plus the absolute value of a plus b end-absolute-value plus the absolute value of b plus c end-absolute-value plus the absolute value of c plus a end-absolute-value close paren is greater than or equal to the absolute value of 3 a plus 3 b plus 3 c plus 3 a plus 3 b plus 3 c end-absolute-value equals the absolute value of 6 a plus 6 b plus 6 c end-absolute-value3(|𝑎|+|𝑏|+|𝑐|+|𝑎+𝑏|+|𝑏+𝑐|+|𝑐+𝑎|)≥|3𝑎+3𝑏+3𝑐+3𝑎+3𝑏+3𝑐|=|6𝑎+6𝑏+6𝑐|.
   • Áp dụng bất đẳng thức tam giác:
   • • |a|+|a|+|a|+|b|+|b|≥|3a+2b|the absolute value of a end-absolute-value plus the absolute value of a end-absolute-value plus the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of b end-absolute-value is greater than or equal to the absolute value of 3 a plus 2 b end-absolute-value|𝑎|+|𝑎|+|𝑎|+|𝑏|+|𝑏|≥|3𝑎+2𝑏|.
     • |a|+|b|+|a+b|≥|2a+2b|the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of a plus b end-absolute-value is greater than or equal to the absolute value of 2 a plus 2 b end-absolute-value|𝑎|+|𝑏|+|𝑎+𝑏|≥|2𝑎+2𝑏|.
   • Xét |5a+4b|=|(a+b)+(a+b)+(a+b)+a+a+b|the absolute value of 5 a plus 4 b end-absolute-value equals the absolute value of open paren a plus b close paren plus open paren a plus b close paren plus open paren a plus b close paren plus a plus a plus b end-absolute-value|5𝑎+4𝑏|=|(𝑎+𝑏)+(𝑎+𝑏)+(𝑎+𝑏)+𝑎+𝑎+𝑏|.
   • Ta có |5a+4b|=|(a+b)+(a+b)+(a+b)+a+a+b|the absolute value of 5 a plus 4 b end-absolute-value equals the absolute value of open paren a plus b close paren plus open paren a plus b close paren plus open paren a plus b close paren plus a plus a plus b end-absolute-value|5𝑎+4𝑏|=|(𝑎+𝑏)+(𝑎+𝑏)+(𝑎+𝑏)+𝑎+𝑎+𝑏|.
   • Áp dụng bất đẳng thức tam giác:
   • • |a|+|b|+|a+b|≥|2a+2b|the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of a plus b end-absolute-value is greater than or equal to the absolute value of 2 a plus 2 b end-absolute-value|𝑎|+|𝑏|+|𝑎+𝑏|≥|2𝑎+2𝑏|.
     • |a|+|b|+|c|+|a+b|+|b+c|+|c+a|≥13|5a+4b|the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of c end-absolute-value plus the absolute value of a plus b end-absolute-value plus the absolute value of b plus c end-absolute-value plus the absolute value of c plus a end-absolute-value is greater than or equal to 1 over 3 end-fraction the absolute value of 5 a plus 4 b end-absolute-value|𝑎|+|𝑏|+|𝑐|+|𝑎+𝑏|+|𝑏+𝑐|+|𝑐+𝑎|≥13|5𝑎+4𝑏|.
   • Ta có 3(|a|+|b|+|a+b|)≥|3a+3b|3 open paren the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of a plus b end-absolute-value close paren is greater than or equal to the absolute value of 3 a plus 3 b end-absolute-value3(|𝑎|+|𝑏|+|𝑎+𝑏|)≥|3𝑎+3𝑏|.
   • Ta có 3(|a|+|b|+|c|+|a+b|+|b+c|+|c+a|)≥|5a+4b|+|5b+4c|+|5c+4a|3 open paren the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of c end-absolute-value plus the absolute value of a plus b end-absolute-value plus the absolute value of b plus c end-absolute-value plus the absolute value of c plus a end-absolute-value close paren is greater than or equal to the absolute value of 5 a plus 4 b end-absolute-value plus the absolute value of 5 b plus 4 c end-absolute-value plus the absolute value of 5 c plus 4 a end-absolute-value3(|𝑎|+|𝑏|+|𝑐|+|𝑎+𝑏|+|𝑏+𝑐|+|𝑐+𝑎|)≥|5𝑎+4𝑏|+|5𝑏+4𝑐|+|5𝑐+4𝑎|.
   • Ta có |a|+|b|+|a+b|≥|2a+2b|the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of a plus b end-absolute-value is greater than or equal to the absolute value of 2 a plus 2 b end-absolute-value|𝑎|+|𝑏|+|𝑎+𝑏|≥|2𝑎+2𝑏|.
   • Ta có |a|+|b|+|c|+|a+b|+|b+c|+|c+a|≥13(|5a+4b|+|5b+4c|+|5c+4a|)the absolute value of a end-absolute-value plus the absolute value of b end-absolute-value plus the absolute value of c end-absolute-value plus the absolute value of a plus b end-absolute-value plus the absolute value of b plus c end-absolute-value plus the absolute value of c plus a end-absolute-value is greater than or equal to 1 over 3 end-fraction open paren the absolute value of 5 a plus 4 b end-absolute-value plus the absolute value of 5 b plus 4 c end-absolute-value plus the absolute value of 5 c plus 4 a end-absolute-value close paren|𝑎|+|𝑏|+|𝑐|+|𝑎+𝑏|+|𝑏+𝑐|+|𝑐+𝑎|≥13(|5𝑎+4𝑏|+|5𝑏+4𝑐|+|5𝑐+4𝑎|).

Áp dụng tính chất tỉ số ta có: \(\frac{a + b + d}{a + b + c + d} > \frac{a + b}{a + b + c} > \frac{a + b}{a + b + c + d} \left(\right. 1 \left.\right)\)

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