Question

Simplifying rational expressions

1. (c+8)(c-8)/(c-8)(c+3)
2. n^2+4n-12/n^2+2n-8
3. 42x^2y^3/28x^3y
4. m^2-3m-10/m-5

Answer 1

1.
`((c + 8)(c - 8))/((c - 8)(c + 3)),`

`(c + 8)/(c + 3)`

2.
`(n^(2) + 4n - 12)/(n^(2) + 2n - 8),`

`(n^(2) + 6n - 2n - 12)/(n^(2) + 4n - 2n - 8),`

`(n(n) + n(6) - 2(n) - 2(6))/(n(n) + n(4) - 2(n) - 2(4)),`

`(n(n + 6) - 2(n + 6))/(n(n + 4) - 2(n + 4)),`

`((n - 2)(n + 6))/((n - 2)(n + 4)),`

`(n + 6)/(n + 4)`

3.
`(42x^(2)y^(3))/(28x^(3)y),`

`(3y^(2))/(2x)`

4.
`(m^(2) - 3m - 10)/(m - 5),`

`(m^(2) - 5m + 2m - 10)/(m - 5),`

`(m(m) - m(5) + 2(m) - 2(5))/(m - 5),`

`(m(m - 5) + 2(m - 5))/(m - 5),`

`((m + 2)(m - 5))/(m - 5),`

`m + 2`