Perform the following operation and express in simplest form. (x^(2)-2x-48)/(6x)*(x-6)/(x^(2)-36) Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator where possible. The numerator x^2 - 2x - 48 can be factored into (x - 8)(x + 6). The denominator x^2 - 36 can be factored into (x - 6)(x + 6) because it is a difference of squares.Write with Factored Terms: Write the expression with the factored terms. The expression now looks like this: ((x - 8)(x + 6))/(6x) * (x - 6)/((x - 6)(x + 6))Cancel Common Terms: Cancel out the common terms. The (x + 6) terms cancel out, as do the (x - 6) terms, as long as x is not equal to -6 or 6 (since division by zero is undefined). The expression simplifies to: (x - 8)/6xCheck for Further Simplification: Check for any further simplification. There are no common factors between the numerator (x - 8) and the denominator 6x, so the expression is already in its simplest form.

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Perform the following operation and express in simplest form.

(x^(2)-2x-48)/(6x)*(x-6)/(x^(2)-36)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}-2 x-48}{6 x} \cdot \frac{x-6}{x^{2}-36}$ $\newline$ 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}-2 x-48}{6 x} \cdot \frac{x-6}{x^{2}-36}

\newline

Answer:

Factor Numerator and Denominator: Factor the numerator and the denominator where possible. $\newline$ The numerator $x^2 - 2x - 48$ can be factored into $(x - 8)(x + 6)$ . $\newline$ The denominator $x^2 - 36$ can be factored into $(x - 6)(x + 6)$ because it is a difference of squares.
Write with Factored Terms: Write the expression with the factored terms. $\newline$ The expression now looks like this: $\newline$ $((x - 8)(x + 6))/(6x) \cdot (x - 6)/((x - 6)(x + 6))$
Cancel Common Terms: Cancel out the common terms. $\newline$ The $(x + 6)$ terms cancel out, as do the $(x - 6)$ terms, as long as $x$ is not equal to $-6$ or $6$ (since division by zero is undefined). $\newline$ The expression simplifies to: $\newline$ $\frac{x - 8}{6x}$
Check for Further Simplification: Check for any further simplification. There are no common factors between the numerator $(x - 8)$ and the denominator $6x$ , so the expression is already in its simplest form.