First, rewrite the term on the right as:
#((x - 5)(x + 5))/(4x^4) -: (2(x - 5))/(8x^5)#
Then rewrite the expression as:
#(((x - 5)(x + 5))/(4x^4))/((2(x - 5))/(8x^5))#
We can now rewrite this expression again using this rule for dividing fractions:
#(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))#
#(color(red)((x - 5)(x + 5))/color(blue)((4x^4)))/(color(green)(2(x - 5))/color(purple)((8x^5))) = (color(red)((x - 5)(x + 5)) xx color(purple)((8x^5)))/(color(blue)((4x^4)) xx color(green)(2(x - 5)))#
We can next cancel some of the common terms in the numerator and denominator:
#(color(red)(cancel((x - 5))(x + 5)) xx color(purple)((cancel(8)x^5)))/(color(blue)((cancel(4)x^4)) xx color(green)(cancel(2)cancel((x - 5)))) = (x^5(x + 5))/x^4#
We can now use these rules of exponents to further simplify the result:
#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #a^color(red)(1) = a#
#(x^color(red)(5)(x + 5))/x^color(blue)(4) = x^(color(red)(5)-color(blue)(4))(x + 5) = x^1(x + 5) = #
#x(x + 5)#
Or
#x^2 + 5x#
However, #(2(x - 5))/(8x^5) != 0#
