Answer:
[tex]\boxed{\dfrac{5}{9}}[/tex]
Step-by-step explanation:
Given expression is
[tex]\dfrac{69}{71} \cdot \dfrac{5}{9} + \dfrac{3}{71}\cdot \dfrac{5}{9} - \dfrac{5}{9}\cdot \dfrac{1}{71}[/tex]
- 5/9 is a common factor so factor outside the expression to get:
[tex]\dfrac{5}{9}\left(\dfrac{69}{71} \cdot 1+ \dfrac{3}{71} \cdot 1- 1. \dfrac{1}{71}\right)\\\\=\dfrac{5}{9}\left(\dfrac{69}{71}+ \dfrac{3}{71} - \dfrac{1}{71}\right)\\[/tex] - 71 on the denominator is common to all three expressions in the parenthesis; that means [tex]\dfrac{1}{71}[/tex] can be factored out:
[tex]\dfrac{5}{9}\left(\dfrac{69}{71} \cdot 1+ \dfrac{3}{71} \cdot 1- 1. \dfrac{1}{71}\right)\\\\=\dfrac{5}{9}\left(\dfrac{69}{71}+ \dfrac{3}{71} - \dfrac{1}{71}\right)\\[/tex] - Since the expression in parenthesis has the common denominator 71 we can simply calculate the numerator addition/subtraction and use 71 as the denominator of the result
[tex]\dfrac{5}{9}\left(\dfrac{69}{71}+ \dfrac{3}{71} - \dfrac{1}{71}\right)\\\\= \dfrac{5}{9}\left(\dfrac{69 + 3 - 1}{71}\right)\\\\= \dfrac{5}{9}\left(\dfrac{71}{71}\right)\\\\= \dfrac{5}{9}\left(1\right)\\\\= \dfrac{5}{9}\\\\\text{Answer: \boxed{\dfrac{5}{9}}}[/tex]
