Final answer:
To divide the expression (15y)/(98z) - : (3y)/(196x), follow the order of operations. Simplify the expression within the parentheses, find the common denominator, apply the division, simplify further, and combine like terms. The simplified expression is (27y)/((196zx)(98z)).
Step-by-step explanation:
To divide the expression (15y)/(98z) - : (3y)/(196x), we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).
Step 1: Simplify the expression in the parentheses. (15y)/(98z) - (3y)/(196x) = (15y)/(98z) - (3/2) * (y/x)
Step 2: Find a common denominator for the fractions. The common denominator is 196zx.
Step 3: Apply the division by multiplying the first fraction by the reciprocal of the second fraction. (15y)/(98z) - (3/2) * (y/x) = ((15y)(2))/((98z)(196zx)) - (3y)/(196zx)
Step 4: Simplify the expression further using the properties of fractions and multiplying the numerators and denominators separately. ((30y))/((196zx)(98z)) - (3y)/(196zx)
Step 5: Combine like terms by subtracting the fractions. ((30y) - (3y))/((196zx)(98z)) = (27y)/((196zx)(98z))
Hence, the simplified expression is (27y)/((196zx)(98z)).