Answer:
a+b
Step-by-step explanation:
Consider the given expression
[tex]\dfrac{\dfrac{2}{b}+\dfrac{2}{a}}{\dfrac{2}{ab}}[/tex]
We need to find the expression which is equivalent to the given expression.
Taking LCM on the numerator, we get
[tex]\dfrac{\dfrac{2a+2b}{ab}}{\dfrac{2}{ab}}[/tex]
Taking out the common factor.
[tex]\dfrac{\dfrac{2(a+b)}{ab}}{\dfrac{2}{ab}}[/tex]
According to the property of division,
[tex]\dfrac{\dfrac{a}{b}}{\dfrac{c}{d}}=\dfrac{a}{b}\times \dfrac{d}{c}[/tex]
Using this property we get
[tex]\dfrac{2(a+b)}{ab}\times \dfrac{ab}{2}[/tex]
Cancel out the common factors.
[tex]a+b[/tex]
Therefore, the expression a+b is equivalent to the given expression.
