Question

Please help i have know idea what to do please help and show work so i can understand thank you!

1.) k+3/4k-2 * (12k^2-3)
2.) x^2-16/6x * 7x/x+5
3.) q+5/2 * 4q/q+4
4.)y^2-9/-2y * -5y/y+3
5.)(8x^2-20x+15) divided by (2x-3)
6.)(8x^3-30+21) divided by (4x-6)
7.)(-10m^9-4m-12m^6) divided by 2m^4

Answer 1

1.
`(k + 3)/(4k - 2)(12k^(2) - 3})`

`(k + 3)/(2(2k) - 2(1))(3(4k^(2)) - 3(1))`

`(k + 3)/(2(2k - 1))(3(4k^(2) - 1))`

`(k + 2)/(2(2k - 1))(3(4k^(2) + 2k - 2k - 1))`

`(k + 3)/(2(2k - 1))(3(2k(2k) + 2k(1) - 1(2k) - 1(1))`

`(k + 3)/(2(2k - 1))(3(2k + 1) - 1(2k + 1))`

`(k + 3)/(2(2k - 1))(3(2k - 1)(2k + 1))`

`(3(k + 3)(2k + 1))/(2)`

2.
`((x^(2) - 16)/(6x))((7x)/(x + 5))`

`((x^(2) + 4x - 4x - 16)/(6))((7)/(x + 5))`

`((x(x) + x(4) - 4(x) - 4(4))/(6))((7)/(x + 5))`

`((x(x + 4) - 4(x + 4))/(6))((7)/(x + 5))`

`(((x - 4)(x + 4))/(6))((7)/(x + 5))`

`(7(x - 4)(x + 4))/(6(x + 5))`

3.
`((q + 5)/(2))((4q)/(q + 4))`

`((q + 5)/(1))((2q)/(q + 4))`

`(2q(q + 5))/(q + 4)`

4.
`((y^(2) - 9)/(-2y))((-5y)/(y + 3))`

`((y^(2) + 3y - 3y - 9)/(2))((5)/(y + 3))`

`((y(y) + y(3) - 3(y) - 3(3))/(2))((5)/(y + 3))`

`((y(y + 3) - 3(y + 3))/(2))((5)/(y + 3))`

`(((y - 3)(y + 3))/(2))((5)/(y + 3))`

`((y - 3)/(2))((5)/(1))`

`(5(y - 3))/(2)`

5.
`(8x^(2) - 20x + 15)/(2x - 3)`

6.
`(8x^(3) - 30 + 21)/(4x - 6)`

`(8x^(3) - 9)/(2(2x) - 2(3))`

`(8x^(3) - 9)/(2(2x - 3))`

7.
`(-10m^(9) - 12m^(6) - 4m)/(2m^(4))`

`(-10m^(9))/(2m^(4)) - (12m^(6))/(2m^(4)) - (4m)/(2m^(4))`

`-5m^(5) - 6m^(2) - (2)/(m^(3))`