How do you simplify #((x-4)/(35-5x))/((x+4)/(49-x^2))#?

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Answer 1 · 2017-01-08T16:01:09

The answer is #=((x-4)(7+x))/(5(x+4))#

We use

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

Therefore,

#((x-4)/(35-5x))/((x+4)/(49-x^2))#

#=((x-4))/((35-5x))*((49-x^2))/((x+4))#

#=((x-4)cancel((7-x))(7+x))/(5cancel((7-x))(x+4))#

#=((x-4)(7+x))/(5(x+4))#