How do you multiply #(5x)/7 div(10x^2)/21#?

1 Answer
May 2, 2017

Answer:

See the entire solution process below:

Explanation:

First, rewrite this expression as:

#((5x)/7)/((10x^2)/21)#

Next, use this rule for dividing fractions to again rewrite the expression:

#(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)(5x)/color(blue)(7))/(color(green)(10x^2)/color(purple)(21)) = (color(red)(5x) xx color(purple)(21))/(color(blue)(7) xx color(green)(10x^2)) = (color(red)(5x) xx color(purple)(7 xx 3))/(color(blue)(7) xx color(green)(5x xx 2x))#

Next, cancel common terms in the numerator and denominator:

#(cancel(color(red)(5x)) xx color(purple)(color(black)(cancel(color(purple)(7))) xx 3))/(cancel(color(blue)(7)) xx color(green)(color(black)(cancel(color(green)(5x))) xx 2x)) = 3/(2x)# Where #x != 0#