How do you multiply and simplify #(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9)#?

2 Answers
Barney V.
Sep 19, 2017

#color(magenta)((-x-5)/9#

Explanation:

#((-x-8)(x-1))/((x+8))xx((x+5))/((9x-9))#

#:.=((-x-8)(x-1))/((x+8))xx((x+5))/((9x-9))#

#:.=((-x-8)cancel((x-1)))/((x+8))xx((x+5))/(9cancel((x-1)))#

#:.=((-x-8)(x+5))/((9x+8))#

#:.=(-x^2-13x-40)/(9(x+8))#

#:.=((-x-5)cancel((x+8)))/(9cancel((x+8)))#

#:.color(magenta)(=(-x-5)/9#

Douglas K.
Sep 19, 2017

To multiply fractions, you multiply the numerators and the denominators respectively.
To simply, you cancel any factors that are common to the numerator and denominator.

Explanation:

To multiply fractions, you multiply the numerators and the denominators respectively:

#(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9) = (( - x - 8) ( x - 1)( x + 5) )/(( x + 8)( 9x - 9))#

A common factor becomes obvious if we write #( - x - 8)" as " -1(x+8)#:

#(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9) = (-1(x+8) ( x - 1)( x + 5) )/(( x + 8)( 9x - 9))#

Cancel the common factor:

#(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9) = (-1( x - 1)( x + 5) )/(( 9x - 9))#

Another common factor becomes obvious if we write #9x-9" as "9(x-1)#:

#(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9) = (-1( x - 1)( x + 5) )/(9(x -1))#

Cancel the common factor:

#(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9) = (-1( x + 5))/9#

Move the #-1/9# to the front:

#(( - x - 8) ( x - 1))/( x + 8) xx ( x + 5) / ( 9x - 9) = -1/9(x+5)#

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