Perform the following operation and express in simplest form. (x^(2)-16)/(x^(2)-x-12)*(9x+27)/(4x-32) Answer:

Factor Polynomials: First, factor each polynomial where possible. The numerator x^2 - 16 is a difference of squares and can be factored into (x + 4)(x - 4). The denominator x^2 - x - 12 can be factored into (x - 4)(x + 3) by finding two numbers that multiply to -12 and add to -1. The numerator 9x + 27 is a common factor problem and can be factored into 3(3x + 9), which simplifies further to 3(3)(x + 3) since 9 is also a factor of 3. The denominator 4x - 32 is also a common factor problem and can be factored into 4(x - 8).Rewrite with Factored Terms: Now, rewrite the original expression with the factored terms. ((x + 4)(x - 4))/((x - 4)(x + 3)) * (3(3)(x + 3))/(4(x - 8))Cancel Common Factors: Next, cancel out the common factors from the numerator and the denominator. The (x - 4) terms cancel each other, and the (x + 3) terms cancel each other. This leaves us with: ((x + 4) * 3 * 3)/(4 * (x - 8))Simplify Expression: Simplify the remaining expression by multiplying the constants together. 3 * 3 = 9, so the expression becomes: (9(x + 4))/(4(x - 8))Final Simplified Form: The expression is now simplified as much as possible, and there are no common factors left to cancel. The final simplified form is: (9(x + 4))/(4(x - 8))

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Perform the following operation and express in simplest form.

(x^(2)-16)/(x^(2)-x-12)*(9x+27)/(4x-32)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-16}{x^{2}-x-12} \cdot \frac{9 x+27}{4 x-32}$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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

\newline

\frac{x^{2}-16}{x^{2}-x-12} \cdot \frac{9 x+27}{4 x-32}

\newline

Answer:

Factor Polynomials: First, factor each polynomial where possible. $\newline$ The numerator $x^2 - 16$ is a difference of squares and can be factored into $(x + 4)(x - 4)$ . $\newline$ The denominator $x^2 - x - 12$ can be factored into $(x - 4)(x + 3)$ by finding two numbers that multiply to $-12$ and add to $-1$ . $\newline$ The numerator $9x + 27$ is a common factor problem and can be factored into $3(3x + 9)$ , which simplifies further to $3(3)(x + 3)$ since $9$ is also a factor of $(x + 4)(x - 4)$ $0$ . $\newline$ The denominator $(x + 4)(x - 4)$ $1$ is also a common factor problem and can be factored into $(x + 4)(x - 4)$ $2$ .
Rewrite with Factored Terms: Now, rewrite the original expression with the factored terms. $\frac{(x + 4)(x - 4)}{(x - 4)(x + 3)} \times \frac{3(3)(x + 3)}{4(x - 8)}$
Cancel Common Factors: Next, cancel out the common factors from the numerator and the denominator. $\newline$ The $(x - 4)$ terms cancel each other, and the $(x + 3)$ terms cancel each other. $\newline$ This leaves us with: $\newline$ $\frac{(x + 4) \cdot 3 \cdot 3}{4 \cdot (x - 8)}$
Simplify Expression: Simplify the remaining expression by multiplying the constants together. $\newline$ $3 \times 3 = 9$ , so the expression becomes: $\newline$ $\frac{9(x + 4)}{4(x - 8)}$
Final Simplified Form: The expression is now simplified as much as possible, and there are no common factors left to cancel. $\newline$ The final simplified form is: $\newline$ $(9(x + 4))/(4(x - 8))$