Question

Tìm x

\(\frac{x+1}{2x+1}=\frac{0.5x+2}{x+3}\)

Answer 1

\(\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}\Rightarrow\left(x+1\right)\left(x+3\right)=\left(0,5x+2\right)\left(2x+1\right)\)

\(\Rightarrow x^2+3x+x+3=x^2+0,5x+4x+2\)

\(\Rightarrow x^2+3x+x-x^2-0,5x-4x=2-3\)

\(\Rightarrow-\frac{1}{2}x=-1\)

\(\Rightarrow x=2\)

Answer 2

\(\frac{x+1}{2x+1}=\frac{0,5x+2}{x+3}\)

\(\Rightarrow\left(x+1\right)\left(x+3\right)=\left(2x+1\right)\left(0,5x+2\right)\)

\(\Rightarrow x^2+3x+x+3=x^2+4x+0,5x+2\)

\(\Rightarrow x^2+3x+x+3-x^2-4x-0,5x-2=0\)

\(\Rightarrow1-0,5x=0\)

\(\Rightarrow\frac{1}{2}x=1\Leftrightarrow x=2\)