Answer:
[tex]5ab[/tex]
Step-by-step explanation:
Given rational expression,
[tex]\frac{20a^2b}{5ab^2}[/tex]
Let x be the expression by which on dividing both the numerator and the denominator the result is [tex]\frac{4a}{b}[/tex]
That is,
[tex]\frac{\frac{20a^2b}{x}}{\frac{5ab^2}{x}}=\frac{4a}{b}[/tex]
By comparing numerators,
[tex]\frac{20a^2b}{x}=4a[/tex]
[tex]20a^2b=4ax[/tex] ( By cross multiplication )
[tex]\implies x = \frac{20a^2b}{4a}=5a^{2-1}b^2=5ab[/tex]
Note : We can get the answer by comparing denominators.
