Question

How do you simplify `(4 - sqrt 7) /(3+sqrt7)`?

Answer 1

`19/2-7/2sqrt7`

Explanation:

`"multiply the numerator/denominator by the conjugate of"`
`"the denominator"`

`"the conjugate of "3+sqrt7" is "3color(red)(-)sqrt7`

`=((4-sqrt7)(3-sqrt7))/((3+sqrt7)(3-sqrt7))`

`=(12-7sqrt7+7)/(9-7)`

`=(19-7sqrt7)/2=19/2-7/2sqrt7`

Answer 2

`frac{19-7\sqrt7}{2}`

Explanation:

`\frac{4-\sqrt7}{3+\sqrt7}`

`=\frac{(4-\sqrt7)(3-\sqrt7)}{(3+\sqrt7)(3-\sqrt7)}`

`=\frac{12-3\sqrt7-4\sqrt7+7}{3^2-(\sqrt7)^2}`

`=\frac{19-7\sqrt7}{9-7}`

`=\frac{19-7\sqrt7}{2}`