Question

tìm biểu thức\(\frac{3x^2-2x-5}{M}=\frac{3x-5}{2x-3}\)

Answer 1

\(\frac{3x^2-2x-5}{M}=\frac{3x-5}{2x-3}\)

Xét VT : \(3x^2-2x-5=\left(3x^2-3\right)-\left(2x+2\right)\)

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

\(=\left(x+1\right)\left(3x-5\right)\)

Vì \(\frac{\left(x+1\right)\left(3x-5\right)}{M}=\frac{3x-5}{2x-3}\)

Nên ta có thể suy ra được M sẽ có dạng  \(\left(x+1\right)\left(2x-3\right)\)

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

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