Perform the following operation and express in simplest form. (x^(2)-64)/(x^(2)-x-72)*(4x-36)/(x^(2)+8x) Answer:

Factor Numerator and Denominator: First, factor the numerator of the first fraction and the denominator of the second fraction. The numerator x^2 - 64 is a difference of squares and can be factored into (x + 8)(x - 8). The denominator x^2 - x - 72 can be factored by finding two numbers that multiply to -72 and add up to -1. These numbers are -9 and 8, so the factorization is (x - 9)(x + 8). The numerator 4x - 36 is a common factor problem and can be factored out as 4(x - 9). The denominator x^2 + 8x can be factored by taking out the common factor x, resulting in x(x + 8).Write Expression with Factors: Now, write the expression with the factors found in the previous step: ((x + 8)(x - 8))/((x - 9)(x + 8)) * (4(x - 9))/(x(x + 8))Cancel Common Factors: Next, cancel out the common factors from the numerator and the denominator across the fractions. The (x + 8) terms cancel each other, and the (x - 9) terms cancel each other. This leaves us with: (x - 8)/1 * 4/1Multiply Remaining Terms: Now, multiply the remaining terms: (x - 8) * 4 = 4x - 32

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Perform the following operation and express in simplest form.

(x^(2)-64)/(x^(2)-x-72)*(4x-36)/(x^(2)+8x)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-64}{x^{2}-x-72} \cdot \frac{4 x-36}{x^{2}+8 x}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

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

\newline

\frac{x^{2}-64}{x^{2}-x-72} \cdot \frac{4 x-36}{x^{2}+8 x}

\newline

Answer:

Factor Numerator and Denominator: First, factor the numerator of the first fraction and the denominator of the second fraction. $\newline$ The numerator $x^2 - 64$ is a difference of squares and can be factored into $(x + 8)(x - 8)$ . $\newline$ The denominator $x^2 - x - 72$ can be factored by finding two numbers that multiply to $-72$ and add up to $-1$ . These numbers are $-9$ and $8$ , so the factorization is $(x - 9)(x + 8)$ . $\newline$ The numerator $4x - 36$ is a common factor problem and can be factored out as $4(x - 9)$ . $\newline$ The denominator $(x + 8)(x - 8)$ $0$ can be factored by taking out the common factor $(x + 8)(x - 8)$ $1$ , resulting in $(x + 8)(x - 8)$ $2$ .
Write Expression with Factors: Now, write the expression with the factors found in the previous step: $\frac{(x + 8)(x - 8)}{(x - 9)(x + 8)} \times \frac{4(x - 9)}{x(x + 8)}$
Cancel Common Factors: Next, cancel out the common factors from the numerator and the denominator across the fractions. $\newline$ The $(x + 8)$ terms cancel each other, and the $(x - 9)$ terms cancel each other. $\newline$ This leaves us with: $\newline$ $\frac{x - 8}{1} \times \frac{4}{1}$
Multiply Remaining Terms: Now, multiply the remaining terms: $(x - 8) \times 4 = 4x - 32$