How do you divide #\frac { 2x - 10} { 3x - 21} -: \frac { x - 5} { 4x - 28}#?

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Answer 1 · 2017-02-10T12:58:36

#8/3#

Let's first take the original:

#(2x-10)/(3x-21) -: (x-5)/(4x-28)#

And change the division to multiplication by inverting the second fraction:

#(2x-10)/(3x-21) xx (4x-28)/(x-5)#

Let's now find the factors:

#(2(x-5))/(3(x-7)) xx (4(x-7))/(x-5)#

And now cancel factors:

#(2cancelcolor(red)((x-5)))/(3cancelcolor(brown)((x-7))) xx (4cancelcolor(brown)((x-7)))/cancelcolor(red)((x-5))=(2xx4)/3=8/3#

Answer 2 · 2017-02-10T13:00:45

#2 2/3#

#(2x-10)/(3x-21)-:(x-5)/(4x-28)#

#:.=(2(x-5))/(3(x-7))-:(x-5)/(4(x-7))#

#:.=2(cancel(x-5))^1/(3(cancel(x-7))^1) xx 4(cancel((x-7)))^1/cancel((x-5))^1#

#:.=8/3#

#:.=2 2/3#