Question

Tìm x:

a)\(\frac{x+7}{x+4}=\frac{2}{5}\)

b)\(\frac{2\text{x}-3}{2}=\frac{50}{2\text{x}-3}\)

c)\(\frac{x+1}{x-3}=\frac{x+3}{x+2}\)

Answer 1

a) \(\frac{x+7}{x+4}=\frac{2}{5}\)

\(\Rightarrow5\left(x+7\right)=2\left(x+4\right)\)

\(\Rightarrow5x+35-2x-8=0\)

\(\Rightarrow3x=-27\)

\(\Rightarrow x=-9\)

b) \(\frac{2x-3}{2}=\frac{50}{2x-3}\)

\(\Rightarrow\left(2x-3\right)^2=100\)

\(\Rightarrow\left[\begin{array}{nghiempt}2x-3=10\\2x-3=-10\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}x=\frac{13}{2}\\x=-\frac{7}{2}\end{array}\right.\)

c) \(\frac{x+1}{x-3}=\frac{x+3}{x+2}\)

\(\Rightarrow\left(x+1\right)\left(x+2\right)=\left(x-3\right)\left(x+3\right)\)

\(\Leftrightarrow x^2+3x+2=x^2-9\)

\(\Leftrightarrow3x=-11\)

\(\Leftrightarrow x=-\frac{11}{3}\)