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)