How do you simplify #(x+5)/(x-5) div (x^2-25)/(5-x)#?

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Answer 1 · 2016-08-13T20:49:41

#-1/((x-5))#

#(x+5)/(x-5) div(x^2-25)/(5-x)#

#(x+5)/cancel((x-5))xx(-cancel((x-5)))/(x^2-25)#

#-((x+5))/(x^2-25)#

#"We can write as "-(x+5)/((x-5)(x+5))" so "(x^2-5^2)=(x-5)(x+5)#

#-cancel(x+5)/((x-5)* cancel((x+5))#

#-1/((x-5))#

Answer 2 · 2016-08-13T20:50:56

#(-1)/(x-5) = 1/(5-x)#

The first step in most algebraic fraction problems is to find factors.

#(x+5)/(x-5) color(red)(div)(color(magenta)(x^2-25))/(5-x)" "color(magenta)(x^2-25)"( difference of squares)"#

=#(x+5)/(x-5) color(red)(xx)color(blue)((5-x))/(color(magenta)((x+5)(x-5))#

NOTE: # color(blue)((5-x) = -(x-5))#

=#cancel(x+5)/cancel(x-5) color(red)(xx)color(blue)((-cancel((x-5)^1))/(cancel((x+5))(x-5)#

=#(-1)/(x-5)#

=#1/(5-x)#