\(\frac{5}{x}=\frac{x}{45}\)

=> \(x^2=225\)

<=> \(x=15\)hoặc \(x=-15\)

\(x+\frac{1}{12}=\frac{3}{x+1}\)

<=> \(\frac{12x+1}{12}=\frac{3}{x+1}\)

=> \(12x^2+12x+x+1=36\)

<=> \(12x^2+13x+1=36\)

<=> \(12x^2+13x-35=0\)

<=> \(\left(x-\frac{5}{4}\right)\left(x+\frac{7}{3}\right)=0\)

<=> \(\hept{\begin{cases}x-\frac{5}{4}=0\\x+\frac{7}{3}=0\end{cases}}\)

<=>\(\hept{\begin{cases}x=\frac{5}{4}\\x=\frac{-7}{3}\end{cases}}\)

a)\(\frac{5}{x}=\frac{x}{45}\)

\(\Rightarrow x^2=5.45\)

\(\Rightarrow x^2=225=\orbr{\begin{cases}15^2\\\left(-15\right)^2\end{cases}}\)

\(\Rightarrow x=\orbr{\begin{cases}15\\-15\end{cases}}\)

b) \(\frac{x+1}{12}=\frac{3}{x+1}\)

\(\Rightarrow\left(x+1\right)^2=36\)

\(\Rightarrow x+1=\orbr{\begin{cases}6\\-6\end{cases}}\)

+) \(\frac{5}{x}=\frac{x}{45}\)

\(\Rightarrow x\times x=5\times45\)

\(\Rightarrow x^2=225\)

\(\Rightarrow\orbr{\begin{cases}x^2=15^2\\x^2=\left(-15\right)^2\end{cases}\Rightarrow}\orbr{\begin{cases}x=15\\x=-15\end{cases}}\)

Vậy x = 15 hoặc x = -15

+) \(\frac{x+1}{12}=\frac{3}{x+1}\)

\(\Rightarrow\left(x+1\right)\times\left(x+1\right)=3\times12\)

\(\Rightarrow\left(x+1\right)^2=36\)

\(\Rightarrow\orbr{\begin{cases}\left(x+1\right)^2=6^2\\\left(x+1\right)^2=\left(-6\right)^2\end{cases}\Rightarrow}\orbr{\begin{cases}x+1=6\\x+1=-6\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=-7\end{cases}}\)

Vậy x = 5 hoặc x = -7

_Chúc bạn học tốt_

5/x=x/45

x²= 5.45

x²=225

Vì 15²=225

Nên x=15

x+1/12=3/x+1

==> (x+1)²=12.3

(x+1)²=36

Vì 6²=36

Nên x=6

a)5/x=x/45

=> x^2=5.45=225

=> x=15 hoặc x=-15

b)(x+1)^2=3.12

(x+1)^2=36

th1 x+1=6=> x=5

th2 x+1=-6=>x=-7

\(\frac{5}{x}=\frac{x}{45}\)

\(\Rightarrow5.45=x^2\)

\(\Rightarrow225=x^2\)

\(\Rightarrow x=\pm15\)

Vậy \(x=\pm15\)

\(\frac{x+1}{12}=\frac{3}{x+1}\)

\(\Leftrightarrow\left(x+1\right)^2=12.3\)

\(\Leftrightarrow\left(x+1\right)^2=36\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=6\\x+1=-6\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=-5\end{cases}}}\)

Vậy ...