Perform the following operation and express in simplest form. (x^(3))/(x^(2)-17 x+72)*(x^(2)-64)/(3x+24) Answer:

Factor Quadratic Expressions: Factor the quadratic expressions where possible. We have the expression (x^(3))/(x^(2)-17x+72) * (x^(2)-64)/(3x+24). Let's start by factoring the quadratic expressions in the denominators and the numerator where possible. The quadratic x^2 - 17x + 72 can be factored into (x - 8)(x - 9), because 8 * 9 = 72 and 8 + 9 = 17. The quadratic x^2 - 64 is a difference of squares and can be factored into (x + 8)(x - 8). The linear term 3x + 24 can be factored out as 3(x + 8).Rewrite with Factored Terms: Rewrite the expression with factored terms. Now we rewrite the original expression using the factored forms: (x^(3))/((x - 8)(x - 9)) * ((x + 8)(x - 8))/(3(x + 8))Cancel Common Factors: Cancel out common factors. We can now cancel out the common factors in the numerator and the denominator: The (x - 8) terms cancel out, and one (x + 8) term cancels out. This leaves us with: (x^(3))/((x - 9)) * (1)/(3)Simplify Expression: Simplify the expression. Now we simplify the expression by multiplying the numerators and denominators: (x^(3) * 1)/((x - 9) * 3) This simplifies to: (x^(3))/(3(x - 9))Check for Further Simplification: Check for any further simplification. There are no common factors left to cancel, and the expression is as simple as it can be.

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Perform the following operation and express in simplest form.

(x^(3))/(x^(2)-17 x+72)*(x^(2)-64)/(3x+24)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{3}}{x^{2}-17 x+72} \cdot \frac{x^{2}-64}{3 x+24}$ $\newline$ 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^{3}}{x^{2}-17 x+72} \cdot \frac{x^{2}-64}{3 x+24}

\newline

Answer:

Factor Quadratic Expressions: Factor the quadratic expressions where possible. $\newline$ We have the expression $(\frac{x^{3}}{x^{2}-17x+72}) \times (\frac{x^{2}-64}{3x+24})$ . Let's start by factoring the quadratic expressions in the denominators and the numerator where possible. $\newline$ The quadratic $x^2 - 17x + 72$ can be factored into $(x - 8)(x - 9)$ , because $8 \times 9 = 72$ and $8 + 9 = 17$ . $\newline$ The quadratic $x^2 - 64$ is a difference of squares and can be factored into $(x + 8)(x - 8)$ . $\newline$ The linear term $3x + 24$ can be factored out as $3(x + 8)$ .
Rewrite with Factored Terms: Rewrite the expression with factored terms. $\newline$ Now we rewrite the original expression using the factored forms: $\newline$ $\frac{x^{3}}{(x - 8)(x - 9)} \times \frac{(x + 8)(x - 8)}{3(x + 8)}$
Cancel Common Factors: Cancel out common factors. $\newline$ We can now cancel out the common factors in the numerator and the denominator: $\newline$ The $(x - 8)$ terms cancel out, and one $(x + 8)$ term cancels out. $\newline$ This leaves us with: $\newline$ $\frac{x^{3}}{x - 9} \times \frac{1}{3}$
Simplify Expression: Simplify the expression. $\newline$ Now we simplify the expression by multiplying the numerators and denominators: $\newline$ $\frac{x^{3} \times 1}{(x - 9) \times 3}$ $\newline$ This simplifies to: $\newline$ $\frac{x^{3}}{3(x - 9)}$
Check for Further Simplification: Check for any further simplification. There are no common factors left to cancel, and the expression is as simple as it can be.