Simplify the expression completely if possible. (x^(2)-81)/(2x^(4)-10x^(3)) Answer:

Identify Factors: Identify the common factors in the numerator and the denominator. The numerator x^2 - 81 is a difference of squares and can be factored as (x + 9)(x - 9).Factor Numerator: Factor the numerator using the difference of squares formula. x^2 - 81 = (x + 9)(x - 9)Examine Denominator: Examine the denominator to see if it can be factored. The denominator 2x^4 - 10x^3 has a common factor of 2x^3.Factor Denominator: Factor out the common factor in the denominator. 2x^4 - 10x^3 = 2x^3(x - 5)Write Expression: Write the expression with the factored numerator and denominator. (x^2 - 81)/(2x^4 - 10x^3) = ((x + 9)(x - 9))/(2x^3(x - 5))Look for Factors: Look for common factors that can be canceled out. There are no common factors between the numerator and the denominator that can be canceled.Final Simplified Form: Since there are no common factors to cancel, the expression is already simplified. The final simplified form is ((x + 9)(x - 9))/(2x^3(x - 5)).

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Q. Simplify the expression completely if possible.

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\frac{x^{2}-81}{2 x^{4}-10 x^{3}}

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Answer:

Identify Factors: Identify the common factors in the numerator and the denominator. $\newline$ The numerator $x^2 - 81$ is a difference of squares and can be factored as $(x + 9)(x - 9)$ .
Factor Numerator: Factor the numerator using the difference of squares formula. $\newline$ $x^2 - 81 = (x + 9)(x - 9)$
Examine Denominator: Examine the denominator to see if it can be factored. The denominator $2x^4 - 10x^3$ has a common factor of $2x^3$ .
Factor Denominator: Factor out the common factor in the denominator. $\newline$ $2x^4 - 10x^3 = 2x^3(x - 5)$
Write Expression: Write the expression with the factored numerator and denominator. $\newline$ $(x^2 - 81)/(2x^4 - 10x^3) = ((x + 9)(x - 9))/(2x^3(x - 5))$
Look for Factors: Look for common factors that can be canceled out. There are no common factors between the numerator and the denominator that can be canceled.
Final Simplified Form: Since there are no common factors to cancel, the expression is already simplified. $\newline$ The final simplified form is $\frac{(x + 9)(x - 9)}{2x^3(x - 5)}$ .