Subtract the rational expressions (frac{5x}{x + 2}) and (frac{3x}{x - 2})

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Accepted Answer

Step:1 ：Find a common denominator. The least common denominator (LCD) of (x + 2) and (x - 2) is ((x + 2)(x - 2)) or (x^2 - 4)Step:2 ：Rewrite each fraction with the LCD as the denominator. This gives us (frac{5x(x - 2)}{x^2 - 4} - frac{3x(x + 2)}{x^2 - 4})Step:3 ：Subtract the fractions now that they have the same denominator. This gives us (frac{5x(x - 2) - 3x(x + 2)}{x^2 - 4})Step:4 ：Simplify the numerator, which results in (frac{5x^2 - 10x - 3x^2 - 6x}{x^2 - 4})Step:5 ：Combine like terms in the numerator to get (frac{2x^2 - 16x}{x^2 - 4})Step:6 ：Finally, break down the numerator and denominator to their simplest terms. This gives us (frac{2x(x - 8)}{(x - 2)(x + 2)})

Answer

Step: 1 ：Find a common denominator. The least common denominator (LCD) of (x + 2) and (x - 2) is ((x + 2)(x - 2)) or (x^2 - 4)Step: 2 ：Rewrite each fraction with the LCD as the denominator. This gives us (frac{5x(x - 2)}{x^2 - 4} - frac{3x(x + 2)}{x^2 - 4})Step: 3 ：Subtract the fractions now that they have the same denominator. This gives us (frac{5x(x - 2) - 3x(x + 2)}{x^2 - 4})Step: 4 ：Simplify the numerator, which results in (frac{5x^2 - 10x - 3x^2 - 6x}{x^2 - 4})Step: 5 ：Combine like terms in the numerator to get (frac{2x^2 - 16x}{x^2 - 4})Step: 6 ：Finally, break down the numerator and denominator to their simplest terms. This gives us (frac{2x(x - 8)}{(x - 2)(x + 2)})

Subtract the rational expressions $\frac{5 x}{x + 2}$ and $\frac{3 x}{x - 2}$

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Popular Problems

Subtract the rational expressions 5xx+2 and 3xx−2

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Popular Problems

Subtract the rational expressions $\frac{5 x}{x + 2}$ and $\frac{3 x}{x - 2}$