How do you add or subtract $\frac{x + 6}{5 x + 10} - \frac{x - 2}{4 x + 8}$ $(x+6)/(5x+10) - (x-2)/(4x+8)$ ?

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How do you add or subtract $\frac{x + 6}{5 x + 10} - \frac{x - 2}{4 x + 8}$ $(x+6)/(5x+10) - (x-2)/(4x+8)$ ?

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Answer 1 · 2015-05-25T10:51:15

Notice that the denominator of each of these terms is a simple multiple of $(x + 2)$ $(x+2)$ , so we only need to multiply by constants to make the denominators of the two terms the same:

$\frac{x + 6}{5 x + 10} - \frac{x - 2}{4 x + 8}$ $(x+6)/(5x+10)-(x-2)/(4x+8)$

$= \frac{x + 6}{5 (x + 2)} - \frac{x - 2}{4 (x + 2)}$ $=(x+6)/(5(x+2))-(x-2)/(4(x+2))$

$= \frac{4 \cdot (x + 6)}{4 \cdot 5 (x + 2)} - \frac{5 \cdot (x - 2)}{5 \cdot 4 (x + 2)}$ $=(4*(x+6))/(4*5(x+2))-(5*(x-2))/(5*4(x+2))$

$= \frac{4 (x + 6)}{20 (x + 2)} - \frac{5 (x - 2)}{20 (x + 2)}$ $=(4(x+6))/(20(x+2))-(5(x-2))/(20(x+2))$

$= \frac{4 (x + 6) - 5 (x - 2)}{20 (x + 2)}$ $=(4(x+6)-5(x-2))/(20(x+2))$

$= \frac{4 x + 24 - 5 x + 10}{20 (x + 2)}$ $=(4x+24-5x+10)/(20(x+2))$

$= \frac{14 - x}{20 (x + 2)}$ $=(14-x)/(20(x+2))$

$= \frac{14 - x}{20 x + 40}$ $=(14-x)/(20x+40)$

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How do you add or subtract $\frac{x + 6}{5 x + 10} - \frac{x - 2}{4 x + 8}$ $(x+6)/(5x+10) - (x-2)/(4x+8)$ ?

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