Concept:The numerator and denominator fit the identity a3+b3=(a+b)(a2−ab+b2).Rewrite 8(1.75)3 as (2×1.75)3=(3.5)3, so numerator becomes (3.5)3+13.Denominator (3.5)2−2.5 can be expressed as (3.5)2−3.5+1, which matches a2−ab+b2 with a=3.5,b=1.Explanation:First, simplify the numerator: 8(1.75)3+1=(2×1.75)3+13=(3.5)3+13.Next, simplify the denominator: (3.5)2−2.5=(3.5)2−3.5+1=(3.5)2−(3.5×1)+12.Now the expression is (3.5)2−3.5+1(3.5)3+13.Apply the identity: (3.5)3+13=(3.5+1)[(3.5)2−3.5+1].Cancel the common term (3.5)2−3.5+1 from numerator and denominator.The result is 3.5+1=4.5.Answer:4.5 (Option B).