How do you divide #(5x+15)/(12x-6) div(10x^2)/(18)#?

Question

Ethan Adkins · Accepted Answer

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

Your starting expression looks like this

#(5x + 15)/(12x-6) * 18/(10x^2)#

Factor the numerator and the denominator of the first fraction to get

#(5(x + 3))/(6(x-2))#

The expression will now become

#(color(red)(cancel(color(black)(5)))(x+3))/(color(red)(cancel(color(black)(6)))(x-2)) * (color(red)(cancel(color(black)(18)))3)/(color(red)(cancel(color(black)(10)))2x^2)#

#(x+3)/(x-2) * 3/(2x^2) = color(green)(3/2 * (x+3)/(x-2) * 1/x^2)#

Julia Adams · Answer

undefined To divide (5x+15)/(12x-6) by (10x^2)/(18), you can simplify the expression by multiplying the numerator and denominator of the first fraction by the reciprocal of the second fraction.

First, find the reciprocal of (10x^2)/(18), which is (18)/(10x^2).

Next, multiply the numerator and denominator of (5x+15)/(12x-6) by (18)/(10x^2).

This results in (5x+15)/(12x-6) * (18)/(10x^2).

To simplify further, multiply the numerators and denominators together:

(5x+15)*(18) / (12x-6)*(10x^2).

Simplify the expression in the numerator:

90x + 270 / (12x-6)*(10x^2).

Simplify the expression in the denominator:

(12x-6)*(10x^2) = 120x^3 - 60x^2.

Therefore, the final simplified expression is:

(90x + 270) / (120x^3 - 60x^2).