QuestionAugust 25, 2025

Add and subtract as indicated. Simplify and leave the numerator and denominator in your answer in factored form. (-x)/(x+14)+(x-14)/(x)-(x)/(x-14) Simplify the expression. (-x)/(x+14)+(x-14)/(x)-(x)/(x-14)=square

Add and subtract as indicated. Simplify and leave the numerator and denominator in your answer in factored form. (-x)/(x+14)+(x-14)/(x)-(x)/(x-14) Simplify the expression. (-x)/(x+14)+(x-14)/(x)-(x)/(x-14)=square
Add and subtract as indicated. Simplify and leave the numerator and denominator in your answer in factored form. (-x)/(x+14)+(x-14)/(x)-(x)/(x-14) Simplify the expression. (-x)/(x+14)+(x-14)/(x)-(x)/(x-14)=square

Solution
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Answer

\frac{-2(x^3 - \frac{1}{2}x^2 + 98)}{(x+14)(x)(x-14)} Explanation 1. Find a common denominator The common denominator for x+14, x, and x-14 is (x+14)(x)(x-14). 2. Rewrite each fraction with the common denominator \frac{-x}{x+14} = \frac{-x \cdot x \cdot (x-14)}{(x+14)(x)(x-14)}, \frac{x-14}{x} = \frac{(x-14) \cdot (x+14) \cdot (x-14)}{(x+14)(x)(x-14)}, \frac{-x}{x-14} = \frac{-x \cdot (x+14) \cdot x}{(x+14)(x)(x-14)}. 3. Combine the fractions Combine into a single fraction: \frac{-x^2(x-14) + (x-14)(x+14) - x(x+14)x}{(x+14)(x)(x-14)}. 4. Simplify the numerator Expand and simplify: -x^3 + 14x^2 + (x^2 - 196) - x^3 - 14x^2 = -2x^3 + x^2 - 196. 5. Factor the numerator Factor out the greatest common factor: -2(x^3 - \frac{1}{2}x^2 + 98).

Explanation

1. Find a common denominator<br /> The common denominator for $x+14$, $x$, and $x-14$ is $(x+14)(x)(x-14)$.<br /><br />2. Rewrite each fraction with the common denominator<br /> $\frac{-x}{x+14} = \frac{-x \cdot x \cdot (x-14)}{(x+14)(x)(x-14)}$, $\frac{x-14}{x} = \frac{(x-14) \cdot (x+14) \cdot (x-14)}{(x+14)(x)(x-14)}$, $\frac{-x}{x-14} = \frac{-x \cdot (x+14) \cdot x}{(x+14)(x)(x-14)}$.<br /><br />3. Combine the fractions<br /> Combine into a single fraction: $\frac{-x^2(x-14) + (x-14)(x+14) - x(x+14)x}{(x+14)(x)(x-14)}$.<br /><br />4. Simplify the numerator<br /> Expand and simplify: $-x^3 + 14x^2 + (x^2 - 196) - x^3 - 14x^2 = -2x^3 + x^2 - 196$.<br /><br />5. Factor the numerator<br /> Factor out the greatest common factor: $-2(x^3 - \frac{1}{2}x^2 + 98)$.
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