How do you multiply #\frac { x ^ { 2} - 25} { ( x + 5) ^ { 2} } \cdot \frac { 2x - 10} { 4x - 20}#?

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Answer 1 · 2016-11-16T16:50:58

#(x^2-25)/(x+5)^2*(2x-10)/(4x-20)=(x-5)/(2x+10)#

Let us factorize each term.

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

#(x+5)^2=(x+5)(x+5)#

#2x-10=2(x-5)# and

#4x-20=4(x-5)#

Hence, #(x^2-25)/(x+5)^2*(2x-10)/(4x-20)#

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

= #(cancel((x+5))(x-5))/(cancel((x+5))(x+5))*(cancel2cancel((x-5)))/(2cancel4cancel((x-5)))#

= #(x-5)/(2(x+5))=(x-5)/(2x+10)#