Perform the following operation and express in simplest form. (x^(2)-36)/(x^(2)-6x)*(x^(2))/(x^(2)+2x-24) Answer:

Identify Factors: Identify the factors of the numerator and denominator in each fraction to simplify the expression. (x^2 - 36) can be factored as (x + 6)(x - 6) because it is a difference of squares. (x^2 - 6x) can be factored as x(x - 6) by taking out the common factor x. (x^2 + 2x - 24) can be factored as (x + 6)(x - 4) by finding two numbers that multiply to -24 and add to 2.Rewrite with Factored Forms: Rewrite the original expression with the factored forms. [(x + 6)(x - 6)] / [x(x - 6)] * [x^2] / [(x + 6)(x - 4)]Cancel Common Factors: Cancel out the common factors from the numerator and denominator. The (x - 6) terms cancel out, and one (x + 6) term cancels out. We are left with: 1 / x * x^2 / (x - 4)Simplify Remaining Expression: Simplify the remaining expression. The x in the denominator and one x from x^2 in the numerator cancel out. We are left with: x / (x - 4)Check for Further Simplification: Check for any further simplification. Since x cannot be factored further and there are no common factors left, the expression is now in its simplest form.

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Perform the following operation and express in simplest form.

(x^(2)-36)/(x^(2)-6x)*(x^(2))/(x^(2)+2x-24)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-36}{x^{2}-6 x} \cdot \frac{x^{2}}{x^{2}+2 x-24}$ $\newline$ 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^{2}-36}{x^{2}-6 x} \cdot \frac{x^{2}}{x^{2}+2 x-24}

\newline

Answer:

Identify Factors: Identify the factors of the numerator and denominator in each fraction to simplify the expression. $\newline$ $(x^2 - 36)$ can be factored as $(x + 6)(x - 6)$ because it is a difference of squares. $\newline$ $(x^2 - 6x)$ can be factored as $x(x - 6)$ by taking out the common factor $x$ . $\newline$ $(x^2 + 2x - 24)$ can be factored as $(x + 6)(x - 4)$ by finding two numbers that multiply to $-24$ and add to $2$ .
Rewrite with Factored Forms: Rewrite the original expression with the factored forms. $[\frac{(x + 6)(x - 6)}{x(x - 6)} \times \frac{x^2}{(x + 6)(x - 4)}]$
Cancel Common Factors: Cancel out the common factors from the numerator and denominator. $\newline$ The $(x - 6)$ terms cancel out, and one $(x + 6)$ term cancels out. $\newline$ We are left with: $\newline$ $\frac{1}{x} \times \frac{x^2}{(x - 4)}$
Simplify Remaining Expression: Simplify the remaining expression. $\newline$ The $x$ in the denominator and one $x$ from $x^2$ in the numerator cancel out. $\newline$ We are left with: $\newline$ $\frac{x}{x - 4}$
Check for Further Simplification: Check for any further simplification. Since $x$ cannot be factored further and there are no common factors left, the expression is now in its simplest form.