How do you simplify #frac{x^{2}+2x-80}{x^{2}-100}\cdot \frac{x^{2}-9x-10}{x^{2}-4x-32}#?

1 Answer
ali ergin
Jun 14, 2017

#"answer "(x+1)/(x+4)#

Explanation:

#(x^2+2x-80)/(x^2-100)*(x^2-9x-10)/(x^2-4x-32)#
#"Please remember the following mathematical identities."#

#x^2+2x-80=(x+10)(x-8)#
#x^2-100=x^2-10^2=(x-10)(x+10)#
#x^2-9x-10=(x-10)(x+1)#
#x^2-4x-32=(x-8)(x+4)#
#"let us write the equation again."#
#((x+10)(x-8))/((x-10)(x+10))*((x-10)(x+1))/((x-8)(x+4))#

#"let us simplify."#

#(cancel((x+10))cancel((x-8)))/(cancel((x+10))cancel((x-10)))*(cancel((x-10))(x+1))/(cancel((x-8))(x+4))#

#"we get;"#
#(x+1)/(x+4)#

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