Perform the following operation and express in simplest form. (x^(3)+2x^(2))/(6x)÷(x^(2)+9x+14)/(x^(2)-49) Answer:

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Perform the following operation and express in simplest form.  (x^(3)+2x^(2))/(6x)÷(x^(2)+9x+14)/(x^(2)-49) Answer:

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Rewrite as multiplication: First, we need to rewrite the division of the two fractions as a multiplication by the reciprocal of the second fraction. (x^(3)+2x^(2))/(6x) ÷ (x^(2)+9x+14)/(x^(2)-49) = (x^(3)+2x^(2))/(6x) * (x^(2)-49)/(x^(2)+9x+14)Factor polynomials: Next, we should factor the polynomials in the numerators and denominators where possible. The numerator x^(3)+2x^(2) can be factored as x^2(x+2). The denominator 6x is already factored. The numerator x^(2)-49 is a difference of squares and can be factored as (x+7)(x-7). The denominator x^(2)+9x+14 can be factored as (x+7)(x+2). So, the expression becomes: (x^2(x+2))/(6x) * ((x+7)(x-7))/((x+7)(x+2))Cancel common factors: Now, we can cancel out the common factors in the numerator and the denominator. The x in the denominator of the first fraction cancels with one x from x^2 in the numerator. The (x+7) and (x+2) terms cancel out between the second fraction's numerator and denominator. This leaves us with: (x)/(6) * (x-7)Multiply remaining terms: Finally, we multiply the remaining terms. (x)/(6) * (x-7) = (x^2-7x)/6 This is the simplified form of the original expression.

Perform the following operation and express in simplest form. $\newline$ $\frac{x^{3}+2 x^{2}}{6 x} \div \frac{x^{2}+9 x+14}{x^{2}-49}$ $\newline$ Answer:

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Perform the following operation and express in simplest form. $\newline$ $\frac{x^{3}+2 x^{2}}{6 x} \div \frac{x^{2}+9 x+14}{x^{2}-49}$ $\newline$ Answer: