How do you simplify #\frac { 3( x + 5) } { 5x ( x + 5) } \cdot \frac { 5} { 3( x - 3) }#?

1 Answer
Apr 10, 2018

#1/(x^2-3x)#

Explanation:

Since this is all multiplication, you can multiply the numerators and denominators. You will realize that there are a lot of similar terms which you can "cancel." These will be highlighted in various colours.

#(color(green)3color(red)((x+5)))/(color(blue)5xcolor(red)((x+5)))*color(blue)5/(color(green)3(x-3)#

To make this more clear, you can rearrange the expression so that the similar terms go on top of each other.

#(color(green)3color(red)((x+5)))/(color(green)3color(red)((x+5)))*color(blue)5/(color(blue)5x(x-3)#

Divisibility rules tell us that #x/x=1# if #x!=0#

Therefore, the term #(color(green)3color(red)((x+5)))/(color(green)3color(red)((x+5)))# is simply 1.

#=1*color(blue)5/(color(blue)5x(x-3)#

Note that we can also "cancel" or divide the two fives together. Remember that the division leaves the number #1# rather than it simply "disappearing."

#=cancelcolor(blue)5^1/(cancelcolor(blue)5^1x(x-3)#

#1/(1*x(x-3)#

Through the distributive property, #x(x-3)=x^2-3x#

Your final answer is #1/(x^2-3x)#