Perform the following operation and express in simplest form. (x^(2)-11 x+28)/(x^(2)-16)*(x^(2)+4x)/(x-4) Answer:

Factor Quadratic Expressions: First, factor the quadratic expressions where possible. The numerator x^2 - 11x + 28 can be factored into (x - 7)(x - 4). The denominator x^2 - 16 is a difference of squares and can be factored into (x - 4)(x + 4).Write Factored Expression: Now, write the expression with the factored forms: ((x - 7)(x - 4))/(x^2 - 16) * (x^2 + 4x)/(x - 4) Replace the factored form of x^2 - 16 into (x - 4)(x + 4): ((x - 7)(x - 4))/((x - 4)(x + 4)) * (x^2 + 4x)/(x - 4)Cancel Common Factors: Next, cancel out the common factors in the numerator and the denominator. The (x - 4) term is present in both the numerator and the denominator, so they cancel each other out. After canceling, the expression becomes: (x - 7)/(x + 4) * (x^2 + 4x)/(x - 4) Now, cancel out the (x - 4) term in the second fraction: (x - 7)/(x + 4) * x(x + 4)/(x - 4)Simplify Expression: After canceling, we see that the (x + 4) term is also present in both the numerator and the denominator, so they cancel each other out as well. The expression simplifies to: (x - 7) * xMultiply Remaining Terms: Finally, multiply out the remaining terms: x(x - 7) = x^2 - 7x This is the simplified form of the original expression.

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Perform the following operation and express in simplest form.

(x^(2)-11 x+28)/(x^(2)-16)*(x^(2)+4x)/(x-4)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-11 x+28}{x^{2}-16} \cdot \frac{x^{2}+4 x}{x-4}$ $\newline$ 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}-11 x+28}{x^{2}-16} \cdot \frac{x^{2}+4 x}{x-4}

\newline

Answer:

Factor Quadratic Expressions: First, factor the quadratic expressions where possible. $\newline$ The numerator $x^2 - 11x + 28$ can be factored into $(x - 7)(x - 4)$ . $\newline$ The denominator $x^2 - 16$ is a difference of squares and can be factored into $(x - 4)(x + 4)$ .
Write Factored Expression: Now, write the expression with the factored forms: $\newline$ $((x - 7)(x - 4))/(x^2 - 16) * (x^2 + 4x)/(x - 4)$ $\newline$ Replace the factored form of $x^2 - 16$ into $(x - 4)(x + 4)$ : $\newline$ $((x - 7)(x - 4))/((x - 4)(x + 4)) * (x^2 + 4x)/(x - 4)$
Cancel Common Factors: Next, cancel out the common factors in the numerator and the denominator. $\newline$ The $(x - 4)$ term is present in both the numerator and the denominator, so they cancel each other out. $\newline$ After canceling, the expression becomes: $\newline$ $\frac{x - 7}{x + 4} \times \frac{x^2 + 4x}{x - 4}$ $\newline$ Now, cancel out the $(x - 4)$ term in the second fraction: $\newline$ $\frac{x - 7}{x + 4} \times \frac{x(x + 4)}{x - 4}$
Simplify Expression: After canceling, we see that the $(x + 4)$ term is also present in both the numerator and the denominator, so they cancel each other out as well. $\newline$ The expression simplifies to: $\newline$ $(x - 7) \times x$
Multiply Remaining Terms: Finally, multiply out the remaining terms: $\newline$ $x(x - 7) = x^2 - 7x$ $\newline$ This is the simplified form of the original expression.