Question

$\frac{x^{2}-12x + 20}{x - 2}$
$(x^{2}+2x + 1)\div(x + 1)$

Explanation:

Step1: Factor numerator (first expression)

$x^2 -12x +20 = (x-10)(x-2)$

Step2: Simplify first rational expression

$\frac{(x-10)(x-2)}{x-2} = x-10$ (where $x
eq 2$)

Step3: Factor numerator (second expression)

$x^2 +2x +1 = (x+1)^2$

Step4: Rewrite division as multiplication

$(x+1)^2 \div (x+1) = \frac{(x+1)^2}{1} \times \frac{1}{x+1}$

Step5: Simplify second expression

$\frac{(x+1)^2}{x+1} = x+1$ (where $x
eq -1$)

Answer:

Simplified first expression: $x-10$ ($x
eq 2$)
Simplified second expression: $x+1$ ($x
eq -1$)