a) \(\Leftrightarrow\dfrac{15x}{x^2+3x-4}-1=\dfrac{12}{x+4}+\dfrac{4}{x-1}\)
\(\Leftrightarrow\dfrac{15x}{x^2+4x-x-4}-\dfrac{12}{x+4}-\dfrac{4}{x-1}=1\)
\(\Leftrightarrow\dfrac{15x}{\left(x-1\right)\left(x+4\right)}-\dfrac{12}{x+4}-\dfrac{4}{x-1}=1\)
\(\Leftrightarrow\dfrac{15x-12x+12-4x-16}{\left(x-1\right)\left(x+4\right)}=1\)
\(\Leftrightarrow\dfrac{-1}{x-1}=1\)
\(\Leftrightarrow x-1=-1\)
\(\Rightarrow x=0\)
tick cho t vs hik
b) \(\Leftrightarrow\left|x-2\right|+3=5\)
\(\Leftrightarrow\left|x-2\right|=5-3\)
\(\Leftrightarrow\left|x-2\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=2\\x-2=-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=0\end{matrix}\right.\)
\(\dfrac{15x}{x^2+3x-4}-1=12\left(\dfrac{1}{x+4}+\dfrac{1}{3x-3}\right)\)
\(\Rightarrow\dfrac{15x}{x^2+3x-4}-1=\dfrac{12}{x+4}+\dfrac{12}{3x-3}\)
\(\Rightarrow\dfrac{15}{x^2+3x-4}-1=\dfrac{36x-36}{\left(x+4\right)\left(3x-3\right)}+\dfrac{12x+48}{\left(x+4\right)\left(3x-3\right)}\)
\(\Rightarrow\dfrac{15}{x^2+3x-4}-1=\dfrac{36x-36+12x+48}{\left(x+4\right)\left(3x-3\right)}\)
\(\Rightarrow\dfrac{15}{x^2+3x-4}-1=\dfrac{48x+12}{x\left(3x-3\right)+4\left(3x-3\right)}\)
\(\Rightarrow\dfrac{15}{x^2+3x-4}-1=\dfrac{48x+12}{3x^2-3x+12x-12}\)
\(\Rightarrow\dfrac{15}{x^2+3x-4}=\dfrac{48x+12}{3x^2+9x-12}\)
\(\Rightarrow15\left(3x^2+9x-12\right)=\left(48x+12\right)\left(x^2+3x-4\right)\)
Nhân ra rồi tính là ok
