How do you combine $\frac{x + 2}{5 x^{2}} + \frac{x + 4}{15 x}$ $(x+2)/(5x^2)+(x+4)/(15x)$ ?

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How do you combine $\frac{x + 2}{5 x^{2}} + \frac{x + 4}{15 x}$ $(x+2)/(5x^2)+(x+4)/(15x)$ ?

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Answer 1 · 2016-07-17T08:29:14

$\frac{x^{2} + 7 x + 6}{15 x^{2}}$ $[x^2 + 7x+ 6]/(15x^2)$

Explanation:

Adding fractions requires a common denominator.

The LCD is $15 x^{2}$ $15x^2$

An equivalent fraction for each fraction must be found with the denominator $15 x^{2}$ $15x^2$

$\frac{x + 2}{5 x^{2}} + \frac{x + 4}{15 x}$ $color(magenta)[(x+2)/(5x^2])+color(blue)[(x+4)/(15x)]$

$\frac{x + 2}{5 x^{2}} \times \frac{3}{3} = \frac{3 (x + 2)}{15 x^{2}}$ $color(magenta)[(x+2)/(5x^2) xx 3/3 = (3(x+2))/(15x^2])$

$\frac{x + 4}{15 x} \times \frac{x}{x} = \frac{x (x + 4)}{15 x^{2}}$ $color(blue)[(x+4)/(15x) xx x/x = (x(x+4))/(15x^2)]$
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$\frac{x + 2}{5 x^{2}} + \frac{x + 4}{15 x}$ $color(magenta)[(x+2)/(5x^2])+color(blue)[(x+4)/(15x)]$

= $\frac{3 (x + 2)}{15 x^{2}} + \frac{x (x + 4)}{15 x^{2}}$ $color(magenta)[(3(x+2))/(15x^2)] + color(blue)[(x(x+4))/(15x^2) ]$

= $\frac{3 x + 6 + x^{2} + 4 x}{15 x^{2}}$ $[color(magenta)(3x+6) + color(blue)(x^2+4x])/(15x^2)$

= $\frac{x^{2} + 7 x + 6}{15 x^{2}}$ $[x^2 + 7x+ 6]/(15x^2)$

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How do you combine $\frac{x + 2}{5 x^{2}} + \frac{x + 4}{15 x}$ $(x+2)/(5x^2)+(x+4)/(15x)$ ?

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Explanation:

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