Với \(a\ne0;a\ne-1\), hãy giải phương trình \(\frac{3ab+1}{a}x=\frac{3ab}{a+1}+\frac{\left(2a+1\right)x}{a\left(a+1\right)^2}+\frac{a^2}{\left(a+1\right)^3}\)
\(x=\frac{a+1}{a}\).\(x=\frac{a-1}{a}\).\(x=\frac{a}{a+1}\).\(x=\frac{a}{a-1}\).Hướng dẫn giải:
Ta có \(\dfrac{3ab+1}{a}x=\dfrac{3ab}{a+1}+\dfrac{\left(2a+1\right)x}{a\left(a+1\right)^2}+\dfrac{a^2}{\left(a+1\right)^3}\) \(\Leftrightarrow[\dfrac{3ab+1}{a}-\dfrac{2a+1}{a\left(a+1\right)^2}]x=\dfrac{3ab}{a+1}+\dfrac{a^2}{\left(a+1\right)^3}\)
\(\Leftrightarrow\dfrac{\left(3ab+1\right)\left(a+1\right)^2-2a-1}{a\left(a+1\right)^2}x=\dfrac{3ab\left(a+1\right)^2+a^2}{\left(a+1\right)^3}\) \(\Leftrightarrow\dfrac{3ab\left(a+1\right)^2+a^2}{a\left(a+1^2\right)}x=\dfrac{3ab\left(a+1\right)^2+a^2}{\left(a+1\right)^3}\) \(\Leftrightarrow x=\dfrac{a}{a+1}\)
Đáp số: \(x=\dfrac{a}{a+1}\)