Simplify the following expression completely. (x^(2)-8x+15)/(x^(2)+3x-40) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. The numerator x^2 - 8x + 15 can be factored into (x - 3)(x - 5) because (x - 3)(x - 5) = x^2 - 5x - 3x + 15 = x^2 - 8x + 15. The denominator x^2 + 3x - 40 can be factored into (x + 8)(x - 5) because (x + 8)(x - 5) = x^2 - 5x + 8x - 40 = x^2 + 3x - 40.Rewrite with Factored Forms: Rewrite the expression with the factored forms. The expression becomes: ((x - 3)(x - 5))/((x + 8)(x - 5))Cancel Common Factors: Cancel out the common factors. The (x - 5) term is present in both the numerator and the denominator, so they cancel each other out. The expression simplifies to: (x - 3)/(x + 8)Check for Further Simplification: Check for any further simplification. There are no common factors left, and neither the numerator nor the denominator can be factored further. Therefore, the expression is fully simplified.

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Simplify the following expression completely.

(x^(2)-8x+15)/(x^(2)+3x-40)
Answer:

Simplify the following expression completely. $\newline$ $\frac{x^{2}-8 x+15}{x^{2}+3 x-40}$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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Q. Simplify the following expression completely.

\newline

\frac{x^{2}-8 x+15}{x^{2}+3 x-40}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator. $\newline$ The numerator $x^2 - 8x + 15$ can be factored into $(x - 3)(x - 5)$ because $(x - 3)(x - 5) = x^2 - 5x - 3x + 15 = x^2 - 8x + 15$ . $\newline$ The denominator $x^2 + 3x - 40$ can be factored into $(x + 8)(x - 5)$ because $(x + 8)(x - 5) = x^2 - 5x + 8x - 40 = x^2 + 3x - 40$ .
Rewrite with Factored Forms: Rewrite the expression with the factored forms. $\newline$ The expression becomes: $\newline$ $\frac{(x - 3)(x - 5)}{(x + 8)(x - 5)}$
Cancel Common Factors: Cancel out the common factors. $\newline$ The $(x - 5)$ term is present in both the numerator and the denominator, so they cancel each other out. $\newline$ The expression simplifies to: $\newline$ $(x - 3)/(x + 8)$
Check for Further Simplification: Check for any further simplification. There are no common factors left, and neither the numerator nor the denominator can be factored further. Therefore, the expression is fully simplified.