Question

simplify the following expression.
\\(\frac{(y - 10)^2}{12} div \frac{12y - 120}{144}\\)

a. \\(\frac{(y - 10)^3}{144}\\)

b. \\(\frac{12(y - 10)^2}{12y - 120}\\)

c. \\(\frac{1}{y - 10}\\)

d. \\(y - 10\\)

Explanation:

Step1: Rewrite division as multiplication

To divide by a fraction, multiply by its reciprocal. So, \(\frac{(y - 10)^2}{12}\div\frac{12y - 120}{144}=\frac{(y - 10)^2}{12}\times\frac{144}{12y - 120}\)

Step2: Factor the numerator of the second fraction

Factor out 12 from \(12y - 120\), we get \(12(y - 10)\). So the expression becomes \(\frac{(y - 10)^2}{12}\times\frac{144}{12(y - 10)}\)

Step3: Simplify the constants and the like terms

Simplify \(\frac{144}{12\times12} = 1\) and \(\frac{(y - 10)^2}{(y - 10)}=(y - 10)\). So after simplifying, we have \((y - 10)\)

Answer:

D. \(y - 10\)