Simplify the expression completely if possible. (x^(2)-25)/(2x^(3)+10x^(2)) Answer:

Identify Factors: Identify the common factors in the numerator and the denominator. The numerator x^2 - 25 is a difference of squares and can be factored as (x + 5)(x - 5). The denominator 2x^3 + 10x^2 can be factored by taking out the common factor of 2x^2, resulting in 2x^2(x + 5).Factorize Numerator: Rewrite the original expression with the factored forms of the numerator and the denominator. The expression becomes ((x + 5)(x - 5)) / (2x^2(x + 5)).Rewrite Expression: Cancel out the common factors in the numerator and the denominator. The (x + 5) term is present in both the numerator and the denominator, so they cancel each other out. The expression simplifies to (x - 5) / (2x^2).Cancel Common Factors: Check for any further simplification. There are no more common factors, and the expression cannot be simplified further.

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Q. Simplify the expression completely if possible.

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\frac{x^{2}-25}{2 x^{3}+10 x^{2}}

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Answer:

Identify Factors: Identify the common factors in the numerator and the denominator. $\newline$ The numerator $x^2 - 25$ is a difference of squares and can be factored as $(x + 5)(x - 5)$ . $\newline$ The denominator $2x^3 + 10x^2$ can be factored by taking out the common factor of $2x^2$ , resulting in $2x^2(x + 5)$ .
Factorize Numerator: Rewrite the original expression with the factored forms of the numerator and the denominator. $\newline$ The expression becomes $\frac{(x + 5)(x - 5)}{2x^2(x + 5)}$ .
Rewrite Expression: Cancel out the common factors in the numerator and the denominator. $\newline$ The $(x + 5)$ term is present in both the numerator and the denominator, so they cancel each other out. $\newline$ The expression simplifies to $(x - 5) / (2x^2)$ .
Cancel Common Factors: Check for any further simplification. $\newline$ There are no more common factors, and the expression cannot be simplified further.