Simplify the expression: (x^2 - 81) / (x^2 - 9x) * (x^2 + 11x + 30) / (x^2 - 36) * (x - 6) / (x + 9) a. (x...

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4. Simplify the expression: (x^2 - 81) / (x^2 - 9x) * (x^2 + 11x + 30) / (x^2 - 36) * (x - 6) / (x + 9) a. (x - 9)(x + 5) / x b. (x + 5) / x c. (x + 9) / x d. (x + 5) / (x(x - 6))

SnapAndSolve AI · Accepted Answer

To simplify the expression, factor each part:

x^2 - 81: This is a difference of squares, so it factors to (x - 9)(x + 9).
x^2 - 9x: Factor out an x, giving x(x - 9).
x^2 + 11x + 30: This factors to (x + 5)(x + 6).
x^2 - 36: This is a difference of squares, so it factors to (x - 6)(x + 6).

Substitute the factors back into the expression:

((x - 9)(x + 9) / (x(x - 9))) * ((x + 5)(x + 6) / ((x - 6)(x + 6))) * ((x - 6) / (x + 9))

Cancel common factors:

- (x - 9) cancels with (x - 9)
- (x + 9) cancels with (x + 9)
- (x + 6) cancels with (x + 6)
- (x - 6) cancels with (x - 6)

The simplified expression is:

(x + 5) / x

Therefore, the correct answer is:

b. (x + 5) / x

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Simplify the expression: (x^2 - 81) / (x^2 - 9x) * (x^2 + 11x + 30) / (x^2 - 36) * (x - 6) / (x + 9) a. (x...

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