Question

5) (x ^ 2)/(5x - x ^ 2) - 3/x = (4 - x)/(x - 5)

Answer 1

\(\Leftrightarrow\dfrac{x^2}{5x-x^2}-\dfrac{3}{x}=\dfrac{4-x}{x-5}\)   đk : x khác 0 ; x khác 5

\(\Leftrightarrow\dfrac{x^2}{x\left(5-x\right)}-\dfrac{3}{x}+\dfrac{4-x}{5-x}=0\)

\(\Leftrightarrow\dfrac{x^2}{x\left(5-x\right)}-\dfrac{3\left(5-x\right)}{x\left(5-x\right)}+\dfrac{x\left(4-x\right)}{x\left(5-x\right)}=0\)

\(\Leftrightarrow\dfrac{x^2}{...}-\dfrac{15-3x}{....}+\dfrac{4x-x^2}{....}=0\)

\(\Leftrightarrow x^2-15+3x+4x-x^2=0\)

\(\Leftrightarrow7x-15=0\)

\(\Rightarrow x=\dfrac{15}{7}\)