Question

Reduce the rational expression x^2 - 10x + 21/ x^2 -6x -7 to its lowest term

Answer 1

the rational expression
`(x^2 - 10x +21)/( x^2-6x -7)` to its lowest term is
`(x-3)/( x+1)` .

Explanation:

Here we need to reduce the rational expression x^2 - 10x + 21/ x^2 -6x -7 to its lowest term . Let's find out:

`(x^2 - 10x +21)/( x^2-6x -7)`

⇒
`(x^2 - 7x-3x +21)/( x^2-7x+x -7)`

⇒
`(x(x - 7)-3x +7(3))/( x(x^-7)+x -7)`

⇒
`(x(x - 7)-3(x -7))/( x(x^-7)+1(x -7))`

⇒
`((x-3)(x - 7))/( (x+1)(x^-7))`

⇒
`((x-3)/( (x+1))`

⇒
`(x-3)/( x+1)`

Therefore , the rational expression
`(x^2 - 10x +21)/( x^2-6x -7)` to its lowest term is
`(x-3)/( x+1)` .