Perform the following operation and express in simplest form. (x^(2))/(x^(2)-64)*(x^(2)-10 x+16)/(x-2) Answer:

Factor Quadratic Expressions: Factor the quadratic expressions where possible. The denominator x^2 - 64 is a difference of squares and can be factored as (x + 8)(x - 8). The numerator x^2 - 10x + 16 can be factored as (x - 2)(x - 8) because it is a quadratic expression that factors neatly.Write Factored Expression: Write the expression with the factored forms. The expression now looks like this: (x^2)/[(x + 8)(x - 8)] * [(x - 2)(x - 8)]/(x - 2)Cancel Common Terms: Cancel out the common terms. The (x - 8) term in the numerator and denominator cancels out, as does the (x - 2) term. This leaves us with: x^2/(x + 8)Check Further Simplification: Check for any further simplification. The expression x^2/(x + 8) cannot be simplified further because x^2 is not a multiple of x + 8.

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Perform the following operation and express in simplest form.

(x^(2))/(x^(2)-64)*(x^(2)-10 x+16)/(x-2)
Answer:

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{2}}{x^{2}-64} \cdot \frac{x^{2}-10 x+16}{x-2}$ $\newline$ 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}}{x^{2}-64} \cdot \frac{x^{2}-10 x+16}{x-2}

\newline

Answer:

Factor Quadratic Expressions: Factor the quadratic expressions where possible. $\newline$ The denominator $x^2 - 64$ is a difference of squares and can be factored as $(x + 8)(x - 8)$ . $\newline$ The numerator $x^2 - 10x + 16$ can be factored as $(x - 2)(x - 8)$ because it is a quadratic expression that factors neatly.
Write Factored Expression: Write the expression with the factored forms. $\newline$ The expression now looks like this: $\newline$ $\frac{x^2}{(x + 8)(x - 8)} \times \frac{(x - 2)(x - 8)}{x - 2}$
Cancel Common Terms: Cancel out the common terms. $\newline$ The $(x - 8)$ term in the numerator and denominator cancels out, as does the $(x - 2)$ term. $\newline$ This leaves us with: $\newline$ $\frac{x^2}{(x + 8)}$
Check Further Simplification: Check for any further simplification. $\newline$ The expression $\frac{x^2}{x + 8}$ cannot be simplified further because $x^2$ is not a multiple of $x + 8$ .