Perform the following operation and express in simplest form. (x^(2)+3x-54)/(x^(3)+4x^(2))÷(x^(2)-81)/(x^(3)-9x^(2)) Answer:

Rewrite Division as Multiplication: Rewrite the division as multiplication by the reciprocal. To divide by a fraction, you multiply by its reciprocal. The reciprocal of (x^(2)-81)/(x^(3)-9x^(2)) is (x^(3)-9x^(2))/(x^(2)-81).Set Up with Reciprocal: Set up the expression with the reciprocal. The original expression (x^(2)+3x-54)/(x^(3)+4x^(2)) ÷ (x^(2)-81)/(x^(3)-9x^(2)) becomes (x^(2)+3x-54)/(x^(3)+4x^(2)) * (x^(3)-9x^(2))/(x^(2)-81).Factor Numerator and Denominator: Factor where possible. Factor the numerator and denominator of each fraction. (x^(2)+3x-54) factors to (x+9)(x-6). (x^(3)+4x^(2)) factors to x^(2)(x+4). (x^(2)-81) factors to (x+9)(x-9). (x^(3)-9x^(2)) factors to x^(2)(x-9).Write Expression with Factors: Write the expression with the factors. The expression now looks like this: ((x+9)(x-6))/(x^(2)(x+4)) * (x^(2)(x-9))/((x+9)(x-9)).Cancel Common Factors: Cancel out common factors. Cancel (x+9) and x^(2) from the numerator and denominator. The expression simplifies to ((x-6)/(x+4)) * ((x-9)/(x-9)).Simplify Remaining Expression: Simplify the remaining expression. After canceling out (x-9), we are left with (x-6)/(x+4).

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Perform the following operation and express in simplest form.

(x^(2)+3x-54)/(x^(3)+4x^(2))÷(x^(2)-81)/(x^(3)-9x^(2))
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}+3 x-54}{x^{3}+4 x^{2}} \div \frac{x^{2}-81}{x^{3}-9 x^{2}}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Perform the following operation and express in simplest form.

\newline

\frac{x^{2}+3 x-54}{x^{3}+4 x^{2}} \div \frac{x^{2}-81}{x^{3}-9 x^{2}}

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Answer:

Rewrite Division as Multiplication: Rewrite the division as multiplication by the reciprocal. $\newline$ To divide by a fraction, you multiply by its reciprocal. The reciprocal of $(x^{2}-81)/(x^{3}-9x^{2})$ is $(x^{3}-9x^{2})/(x^{2}-81)$ .
Set Up with Reciprocal: Set up the expression with the reciprocal. $\newline$ The original expression $(x^{2}+3x-54)/(x^{3}+4x^{2}) \div (x^{2}-81)/(x^{3}-9x^{2})$ becomes $(x^{2}+3x-54)/(x^{3}+4x^{2}) \times (x^{3}-9x^{2})/(x^{2}-81)$ .
Factor Numerator and Denominator: Factor where possible. $\newline$ Factor the numerator and denominator of each fraction. $\newline$ $(x^{2}+3x-54)$ factors to $(x+9)(x-6)$ . $\newline$ $(x^{3}+4x^{2})$ factors to $x^{2}(x+4)$ . $\newline$ $(x^{2}-81)$ factors to $(x+9)(x-9)$ . $\newline$ $(x^{3}-9x^{2})$ factors to $x^{2}(x-9)$ .
Write Expression with Factors: Write the expression with the factors. $\newline$ The expression now looks like this: $\frac{(x+9)(x-6)}{x^{2}(x+4)} \times \frac{x^{2}(x-9)}{(x+9)(x-9)}$ .
Cancel Common Factors: Cancel out common factors. Cancel $(x+9)$ and $x^{2}$ from the numerator and denominator. The expression simplifies to $\frac{(x-6)}{(x+4)} \times \frac{(x-9)}{(x-9)}$ .
Simplify Remaining Expression: Simplify the remaining expression. $\newline$ After canceling out $(x-9)$ , we are left with $\frac{x-6}{x+4}$ .