Simplify the following expression completely. (x^(2)-12 x+20)/(x^(2)-14 x+40) Answer:

Identify Expression: Identify the expression to be simplified: (x^(2)-12x+20)/(x^(2)-14x+40).Factor Numerator: Factor the numerator x^(2)-12x+20. Look for two numbers that multiply to 20 and add up to -12. The numbers are -10 and -2. (x^(2)-12x+20) = (x-10)(x-2).Factor Denominator: Factor the denominator x^(2)-14x+40. Look for two numbers that multiply to 40 and add up to -14. The numbers are -10 and -4. (x^(2)-14x+40) = (x-10)(x-4).Write Simplified Form: Write the simplified form of the expression using the factored numerator and denominator. ((x-10)(x-2))/((x-10)(x-4)).Cancel Common Factor: Cancel out the common factor (x-10) from the numerator and the denominator. The simplified expression is (x-2)/(x-4).Check Restrictions: Check for any restrictions on the variable x. Since we divided by (x-10), x cannot be 10. Also, the denominator (x-4) means x cannot be 4.

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Q. Simplify the following expression completely.

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\frac{x^{2}-12 x+20}{x^{2}-14 x+40}

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Answer:

Identify Expression: Identify the expression to be simplified: $(x^{2}-12x+20)/(x^{2}-14x+40)$ .
Factor Numerator: Factor the numerator $x^{2}-12x+20$ . Look for two numbers that multiply to $20$ and add up to $-12$ . The numbers are $-10$ and $-2$ . $\newline$ $(x^{2}-12x+20) = (x-10)(x-2)$ .
Factor Denominator: Factor the denominator $x^{2}-14x+40$ . Look for two numbers that multiply to $40$ and add up to $-14$ . The numbers are $-10$ and $-4$ . $\newline$ $(x^{2}-14x+40) = (x-10)(x-4)$ .
Write Simplified Form: Write the simplified form of the expression using the factored numerator and denominator. $\frac{(x-10)(x-2)}{(x-10)(x-4)}$ .
Cancel Common Factor: Cancel out the common factor $(x-10)$ from the numerator and the denominator. $\newline$ The simplified expression is $\frac{x-2}{x-4}$ .
Check Restrictions: Check for any restrictions on the variable $x$ . Since we divided by $(x-10)$ , $x$ cannot be $10$ . Also, the denominator $(x-4)$ means $x$ cannot be $4$ .