How do you multiply and simplify #\frac { 7s } { s ^ { 2} - 64} \cdot \frac { s - 8} { s }#?

1 Answer
smendyka
Mar 22, 2017

See the entire simplification process below:

Explanation:

First, rewrite this expression as:

#(7s * (s - 8))/((s^2 - 64) * s)#

#(s^2 - 64)# can be factored using the standard rule:

#a^2 - b^2 = (a - b)(a + b)#

#(7s * (s - 8))/((s - 8)(s + 8) * s)#

We can now cancel common terms in the numerator and denominator.

#(7color(red)(cancel(color(black)(s))) * color(blue)(cancel(color(black)((s - 8)))))/(color(blue)(cancel(color(black)((s - 8))))(s + 8) * color(red)(cancel(color(black)(s)))) =#

#7/(s + 8)# Where #s# cannot be #0# or #+-8#

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