Question

If you could show as much work as possible that would be amazing!!

if you can do the ones you know how to do you dont have to do them all! thank you all so much!!

Reduce

9. x^2+7x+12/ x^2+11x+28

11. y^3+27/y^2+2y-3

Multiply

19. 12a^9u^7/15c * 3c^4/21a^13u^8

21. x-3/x-7 * x^2-12x+35/x^2+3x-18

Divide

29.k^6/x^2 divided by 2k^4/3x^6

33. x+5/x+1 divided by x^2+11x+30/x^2+3x+2

37. x-10/x+13 divided by x^3 - 1000/ x^2+15x+21

Answer 1

Answers:

Reduce:

Here we gave to simplify the expressions:

9)
`x^(2)+7x+(12)/(x^(2))+11x+28`

Grouping similar terms:

`(x^(2)+(12)/(x^(2)))+(18x+28)`

Applying common factor
`x^(2)` in the first parenthesis and common factor
`2` in the second parenthesis:

`x^(2)(1+(12)/(x^(4)))+2(9x+14)` This is the answer

11)
`y^(3)+(27)/(y^(2))+2y-3`

Rearranging the terms:

`(y^(3)+2y)+((27)/(y^(2))-3)`

Applying common factor
`y` in the first parenthesis and common factor
`3` in the second parenthesis:

`y(y^(2)+2)+3((9)/(y^(2))-1)` This is the answer

Multiply:

19)
`((12a^(9)u^(7))/(15 c))(\frac{3c^(4)}{21a^{13 u^(8)}})`

Multiplying both fractions:

`(36 a^(9)u^(7)c^(4))/(315 c a^(13)u^(8))`

Dividing numerator and denominator by 3 and simplifying:

`(12 c^(3))/(105 c a^(4)u)` This is the answer

21)
`(x-(3)/(x)-7)(x^(2)-9x+(35)/(x^(2))-18)`

`((x^(2)-3-7x)/(x))((x^(4)-9x^(3)+35-18x^(2))/(x^(2)))`

Operating with cross product:

`x^(2) (x^(2)-3-7x) x(x^(4)-9x^(3)+35-18x^(2))`

`x^(9) -9x^(8) -18x^(7)+35x^(5)-7x^(8)  +63x^(7)+126x^(6)-245x^(4)-3x^(7)+27x^(6)+54x^(5)-105x^(3)`

Grouping similar terms and factoring:

`x^(9)-2(8x^(8)+21x^(7) )+153x^(6)+89x^(5)-5(49x^(4)+21x^(3))` This is the answer

Divide:

29)
`((k^(6))/(x^(2)))/((2k^(4))/(3x^(6)))`

`(3k^(6)x^(6))/(2x^(2)k^(4))`

Simplifying:

`(3)/(2) k^(2)x^(4)` This is the answer

33)
`((x+5)/(x+1))/((x^(2)+11x+30)/(x^(2)+3x+2))`

`((x+5)(x^(2)+3x+2))/((x+1)(x^(2)+11x+30))`

Factoring numerator and denominator:

`((x+5)(x+2)(x+1))/((x+1)(x+6)(x+5))`

Simplifying:

`(x+2)/(x+6)` This is the answer

37)
`((x-10)/(x+13))/((x^(3)-1000)/(x^(2)+15x+21))`

`((x-10)(x^(2)+15x+21))/((x+13)(x^(3)-1000))`

Applying the distributive property in numerator and denominator:

`(x^(3)+15x^(2)+21x-10x^(2)-150x-210)/((x+13)(x^(4)-1000x+13x^(3)-13000))`

Grouping similar terms and factoring by common factor:

`-(5x(x^(2)-129)(x^(2)-42))/(1000x^(3) (x+13)(x-13))`

Dividing by
`5` in numerator and denominator and simplifying:

`-((x^(2)-129)(x^(2)-42))/(200x^(2)(x+13)(x-13))` This is the answer