`4  . (1/2 -   x)  -1/3 = 7x - 1/4`

`=> 4 . (1/2 -  x)   - 7x = -1/4 +1/3`

`=>2 - 4x - 7x             = 1/12`

`=>     -11x                  = 2 - 1/12`

`=>     -11x                   = 23/21`

`=>         x                   = -23/132`

`64 xx 4^n = 4^5`

`=> 4^3 xx 4^n = 4^5`

`=>             4^n = 4^5 : 4^3`

`=>             4^n = 4^2`

`=>                n  = 2`

`x` x `6,3 = 187`

`=> x    = 187 : 6,3`

`=> x     = 1870/63`

\(\dfrac{11}{9}-\dfrac{4}{3}+\dfrac{7}{9}\)

\(=\dfrac{11}{9}-\dfrac{12}{9}+\dfrac{7}{9}\)

\(=\dfrac{11-12+7}{9}\)

\(=\dfrac{6}{9}=\dfrac{2}{3}\)

`(2x+1)^2 = 100`

`=> (2x + 1)^2 = 10^2`

`=>` \(\left[{}\begin{matrix}2x+1=10\\2x+1=-10\end{matrix}\right.\)

`<=>`\(\left[{}\begin{matrix}2x=9\\2x=-11\end{matrix}\right.\)

`<=>` \(\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=-\dfrac{11}{2}\end{matrix}\right.\)

\(5^{11}.5^4=5^{11+4}=5^{15}\)

\(11^7.11^5=11^{7+5}=11^{12}\)

`\(3.9.27.81=3^1.3^2.3^3.3^4=3^{1+2+3+4}=3^{10}\)

\(5^{16}:5^{12}.5^2=5^{16-12+2}=5^6\)

để \(\dfrac{26}{x}+3\) là `1` số nguyên thì:

`=> 26`⋮ `x`

`=> x` ∈ `Ư(26)`

`=> x`∈ `{ 1 ; 2 ; 13 ; 26}`

Vì `3` là số nguyên và \(\dfrac{26}{x}\) cũng là số nguyên nên :

\(\dfrac{26}{x}+3\) là số nguyên .

vậy `x` ∈ `{1 ; 2 ; 13 ; 26}`

\(\dfrac{9}{5}+\dfrac{9}{78}\)

\(=\dfrac{9}{5}+\dfrac{3}{26}\)

\(=\dfrac{234}{130}+\dfrac{15}{130}\)

\(=\dfrac{249}{130}\)

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\(\dfrac{15}{7}+\dfrac{51}{17}\)

\(=\dfrac{15}{7}+3\)

\(=\dfrac{15}{7}+\dfrac{21}{7}\)

\(=\dfrac{36}{7}\)