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=\frac{x^{2}-81}{\frac{1}{x+9}}

(Do not factor.)

Jan 29, 2024

=\frac{x^{2}-81}{\frac{1}{x+9}}

(Do not factor.)

Generated Graph

Solution by Steps

step 1

To simplify the expression, we first recognize that dividing by a fraction is equivalent to multiplying by its reciprocal

step 2

The reciprocal of

\frac{1}{x+9}

x+9

step 3

We multiply the numerator

(x^2 - 81)

by the reciprocal of the denominator

(x+9)

step 4

The expression simplifies to

(x^2 - 81)(x + 9)

step 5

We expand the expression to get

x^3 + 9x^2 - 81x - 729

Answer

x^3 + 9x^2 - 81x - 729

Key Concept

Dividing by a fraction is equivalent to multiplying by its reciprocal.

Explanation

To simplify a complex fraction, we can multiply the numerator by the reciprocal of the denominator. This eliminates the complex fraction and allows us to simplify the expression further.