Question

Tìm x sao cho biểu thức\(\frac{2x-9}{2x-5}+\frac{3x}{3x+2}\) có giá trị bằng 2

Answer 1

\(\Leftrightarrow\frac{2x-9}{2x-5}-1+\frac{3x}{3x+2}-1=0\)

\(\Leftrightarrow\frac{-4}{2x-5}+\frac{-2}{3x+2}=0\)

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

\(\Leftrightarrow\frac{8x-1}{\left(2x-5\right)\left(3x+2\right)}=0\Rightarrow x=\frac{1}{8}\)

Answer 2

ta có :

\(\frac{2x-9}{2x-5}+\frac{3x}{3x+2}=2\\ \Rightarrow\frac{\left(2x-5\right)-4}{2x-5}+\frac{\left(3x+2\right)-2}{3x+2}=2\\ \Rightarrow1-\frac{4}{2x-5}+1-\frac{2}{3x+2}=2\\ \Rightarrow\frac{-4}{2x-5}-\frac{2}{3x+2}=0\\ \Rightarrow\frac{-4}{2x-5}=\frac{2}{3x+2}\\ \Rightarrow-4.\left(3x+2\right)=2.\left(2x-5\right)\\ \Rightarrow-12x-8=4x-10\\ \Rightarrow16x=2\\ \Rightarrow x=\frac{1}{8}\)

vậy ...

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