Question

1. \\(\frac{r^2s + rs^2}{rs}\\)\
2. \\(\frac{18m^2n - 4mn^2}{-2mn}\\)\
3. \\(\frac{14x^6y^3 - 49x^5y^9}{-7x^4y}\\)\
4. \\(\frac{9c^2d^9 - 27c^6d^5 - 3cd^3}{3cd^3}\\)\
5. \\(\frac{-25x^4y^3 + 30x^2y^5}{-5x^2y}\\)\
6. \\(\frac{32s^5w^2 - 24s^2w^3}{8s^2w^2}\\)\
7. \\(\frac{3x^3y + 5x^2y^2 - 2xy}{xy}\\)\
8. \\(\frac{28p^5 - 8p^4 + 40p^2}{4p^3}\\)\
9. \\(\frac{27n^4 - 9n^3 + 63n^2}{9n}\\)\
10. \\(\frac{9x^3y^2 + 15x^2y - 6x^2}{3x^2}\\)\
11. \\(\frac{24w^4 + 14w^3 - 4w^2 + 10w}{2w}\\)\
12. \\(\frac{-10a^3b^2 + 25a^2b^5 - 5a^2b}{-5a^2b}\\)\
13. \\(\frac{12r^3s^5 - 18r^2s^2 + 3rs}{3rs}\\)\
14. \\(\frac{56x^4y^5 - 49x^3y^6 - 35x^2y^3}{7x^2y^2}\\)\
15. \\(\frac{45p^5q^4 - 60p^3q^2 - 15p^2q^3}{15p^2q^2}\\)

Explanation:

Step1: Split fraction into terms

$\frac{r^2s + rs^2}{rs} = \frac{r^2s}{rs} + \frac{rs^2}{rs}$

Step2: Simplify each term

$= r + s$

Step1: Split fraction into terms

$\frac{18m^2n - 4mn^2}{-2mn} = \frac{18m^2n}{-2mn} - \frac{4mn^2}{-2mn}$

Step2: Simplify each term

$= -9m + 2n$

Step1: Split fraction into terms

$\frac{14x^6y^3 - 49x^5y^9}{-7x^4y} = \frac{14x^6y^3}{-7x^4y} - \frac{49x^5y^9}{-7x^4y}$

Step2: Simplify each term

$= -2x^2y^2 + 7xy^8$

Step1: Split fraction into terms

$\frac{9c^2d^9 - 27c^6d^5 - 3cd^3}{3cd^3} = \frac{9c^2d^9}{3cd^3} - \frac{27c^6d^5}{3cd^3} - \frac{3cd^3}{3cd^3}$

Step2: Simplify each term

$= 3cd^6 - 9c^5d^2 - 1$

Answer:

$r + s$

---