How do you solve #(x+4)/(x-1) div (x^2 +x)/(x-1)#?

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Answer 1 · 2016-03-15T04:02:07

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

#1#. Factor the numerator of the second fraction.

#(x+4)/(x-1)-:(x^2+x)/(x-1)#

#=(x+4)/(x-1)-:(x(x+1))/(x-1)#

#2#. Take the reciprocal of the second fraction to change the operation to multiplication.

#=(x+4)/(x-1)*(x-1)/(x(x+1))#

#3#. Cancel out the factors which appear in the numerator and denominator as a pair.

#=(x+4)/color(red)cancelcolor(black)(x-1)*color(red)cancelcolor(black)(x-1)/(x(x+1))#

#4#. Rewrite the expression.

#=color(green)(|bar(ul(color(white)(a/a)(x+4)/(x(x+1))color(white)(a/a)|)))#