Question

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

Answer 1

the  rational expression $\frac{x^2 - 10x +21}{ x^2-6x -7}$  to its lowest term is $\frac{x-3}{ x+1}$ .

Step-by-step 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:

$\frac{x^2 - 10x +21}{ x^2-6x -7}$

⇒ $\frac{x^2 - 7x-3x +21}{ x^2-7x+x -7}$

⇒ $\frac{x(x - 7)-3x +7(3)}{ x(x^-7)+x -7}$

⇒ $\frac{x(x - 7)-3(x -7)}{ x(x^-7)+1(x -7)}$

⇒ $\frac{(x-3)(x - 7)}{ (x+1)(x^-7)}$

⇒ $\frac{(x-3}{ (x+1)}$

⇒ $\frac{x-3}{ x+1}$

Therefore , the  rational expression $\frac{x^2 - 10x +21}{ x^2-6x -7}$  to its lowest term is $\frac{x-3}{ x+1}$ .