Answer:
Option C
Step-by-step explanation:
Difference of the two expressions has been written as,
![\frac{3x}{x^2-7x+10}-\frac{2x}{3(x-5)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7Bx%5E2-7x%2B10%7D-%5Cfrac%7B2x%7D%7B3%28x-5%29%7D)
To rewrite this expression as one expression,
First he factored the the denominators,
![\frac{3x}{(x-2)(x-5)}-\frac{2x}{3(x-5)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B%28x-2%29%28x-5%29%7D-%5Cfrac%7B2x%7D%7B3%28x-5%29%7D)
Then Juan will make the denominators of both the terms equal,
For which he will multiply the second expression by
.
![\frac{3x}{(x-2)(x-5)}-\frac{2x(x-2)}{3(x-5)(x-2)}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B%28x-2%29%28x-5%29%7D-%5Cfrac%7B2x%28x-2%29%7D%7B3%28x-5%29%28x-2%29%7D)
Option C will be the correct option.