![$\frac{(x+1)(x-3)}{x^{2}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%28x%2B1%29%28x-3%29%7D%7Bx%5E%7B2%7D%7D)
Solution:
Given expression:
![$\frac{\frac{36}{x^{2}}+\frac{36}{x}}{\frac{36}{x-3}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cfrac%7B36%7D%7Bx%5E%7B2%7D%7D%2B%5Cfrac%7B36%7D%7Bx%7D%7D%7B%5Cfrac%7B36%7D%7Bx-3%7D%7D)
To solve this expression:
![$\frac{\frac{36}{x^{2}}+\frac{36}{x}}{\frac{36}{x-3}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cfrac%7B36%7D%7Bx%5E%7B2%7D%7D%2B%5Cfrac%7B36%7D%7Bx%7D%7D%7B%5Cfrac%7B36%7D%7Bx-3%7D%7D)
Apply the fraction rule: ![$\frac{a}{\frac{b}{c}}=\frac{a \cdot c}{b}](https://tex.z-dn.net/?f=%24%5Cfrac%7Ba%7D%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%3D%5Cfrac%7Ba%20%5Ccdot%20c%7D%7Bb%7D)
![$=\frac{\left(\frac{36}{x^{2}}+\frac{36}{x}\right)(x-3)}{36}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%5Cleft%28%5Cfrac%7B36%7D%7Bx%5E%7B2%7D%7D%2B%5Cfrac%7B36%7D%7Bx%7D%5Cright%29%28x-3%29%7D%7B36%7D)
Let us solve
.
Least common multiple of
is
.
Make the denominator same based on the LCM.
So that multiply and divide the 2nd term by x, we get
![$\frac{36}{x^{2}}+\frac{36}{x}=\frac{36}{x^{2}}+\frac{36 x}{x^{2}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B36%7D%7Bx%5E%7B2%7D%7D%2B%5Cfrac%7B36%7D%7Bx%7D%3D%5Cfrac%7B36%7D%7Bx%5E%7B2%7D%7D%2B%5Cfrac%7B36%20x%7D%7Bx%5E%7B2%7D%7D)
![$=\frac{36+36 x}{x^{2}}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B36%2B36%20x%7D%7Bx%5E%7B2%7D%7D)
Now, multiply by (x - 3).
![$\frac{36+36 x}{x^{2}}(x-3)= \frac{(36 x+36)(x-3)}{x^{2}}](https://tex.z-dn.net/?f=%24%5Cfrac%7B36%2B36%20x%7D%7Bx%5E%7B2%7D%7D%28x-3%29%3D%20%5Cfrac%7B%2836%20x%2B36%29%28x-3%29%7D%7Bx%5E%7B2%7D%7D)
![$\frac{\left(\frac{36}{x^{2}}+\frac{36}{x}\right)(x-3)}{36}=\frac{\frac{(36 x+36)(x-3)}{x^{2}}}{36}](https://tex.z-dn.net/?f=%24%5Cfrac%7B%5Cleft%28%5Cfrac%7B36%7D%7Bx%5E%7B2%7D%7D%2B%5Cfrac%7B36%7D%7Bx%7D%5Cright%29%28x-3%29%7D%7B36%7D%3D%5Cfrac%7B%5Cfrac%7B%2836%20x%2B36%29%28x-3%29%7D%7Bx%5E%7B2%7D%7D%7D%7B36%7D)
Apply the fraction rule: ![\frac{\frac{b}{c}}{a}=\frac{b}{c \cdot a}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%7Ba%7D%3D%5Cfrac%7Bb%7D%7Bc%20%5Ccdot%20a%7D)
![$=\frac{(36x+36)(x-3)}{x^{2} \cdot 36}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%2836x%2B36%29%28x-3%29%7D%7Bx%5E%7B2%7D%20%5Ccdot%2036%7D)
![$=\frac{36(x+1)(x-3)}{x^{2} \cdot 36}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B36%28x%2B1%29%28x-3%29%7D%7Bx%5E%7B2%7D%20%5Ccdot%2036%7D)
Cancel the common factor 36.
![$=\frac{(x+1)(x-3)}{x^{2}}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B%28x%2B1%29%28x-3%29%7D%7Bx%5E%7B2%7D%7D)
Hence the solution is
.
Answer:
uh... you forgot to add the image...
ask again with a screenshot/picture next time...
The original price of the shirt is $25. In union city, there is a 3.2% discount. So, the discounted price of the shirt at union city is $24.20. In river city, there is a discount of 3% for the same shirt. So, the price of the shirt at river city is $24.25. Therefore, the shirt will cost $0.05 more in river city than in union city.