1.26 Given the expression

$$
\begin{aligned}
& \frac{x^{3}-a^{-\frac{2}{3}} \cdot b^{-1}\left(a^{2}+b^{2}\right) x+b^{\frac{1}{2}}}{b^{\frac{3}{2}} x^{2}} \\
& \text { Substitute } x=a^{\frac{2}{3} b}-\frac{1}{2} \text { and simplify the result }
\end{aligned}
$$

Eliminate the irrationality in the denominator of the fraction (1.27-1.28):
1.26 After performing the specified substitution, we find

$$
\begin{aligned}
& \frac{\left(a^{\frac{2}{3}} b^{-\frac{1}{2}}\right)^{3}-a^{-\frac{2}{3}+\frac{2}{3}} b^{-1-\frac{1}{2}}\left(a^{2}+b^{2}\right)+b^{\frac{1}{2}}}{b^{\frac{3}{2}}\left(a^{\frac{2}{3}} b^{\left.-\frac{1}{2}\right)^{2}}\right.}= \\
& =\frac{a^{2} b^{-\frac{3}{2}}-b^{-\frac{3}{2}} a^{2}-b^{\frac{1}{2}}+b^{\frac{1}{2}}}{a^{\frac{4}{3}} b^{\frac{1}{2}}}=0
\end{aligned}
$$

Answer: 0.