Question

How do you simplify `\frac { r ^ { 2} - 16r + 63} { 6r ^ { 3} - 54r ^ { 2} }`?

Answer 1

`(r - 7)/(6r^2)`

Explanation:

Factor the numerator
`N = r^2 - 16r + 63`
Find 2 numbers knowing the sum (b = -16) and the product (c = 63).
They are - 9 and - 7
N = (r - 9)(r - 7)
Factor the denominator:
`D = 6r^2(r - 9)`
Finally,
`N/D = ((r - 9)(r - 7))/((6r^2)(r - 9)) = (r - 7)/(6r^2)`