How do you simplify $\frac{3}{w + 4} + \frac{8}{3 w} + \frac{12}{w (w + 4)}$ $3/(w + 4) + 8/(3w) + 12/(w(w +4))$ ?

Question

1483 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-05-23T07:18:08

$\frac{3}{w + 4} + \frac{8}{3 w} + \frac{12}{w (w + 4)} = \frac{17}{3 w}$ $3/(w+4)+8/(3w)+12/(w(w+4))=17/(3w)$

In $\frac{3}{w + 4} + \frac{8}{3 w} + \frac{12}{w (w + 4)}$ $3/(w+4)+8/(3w)+12/(w(w+4))$ , we have denominators as

$w + 4$ $w+4$ , $3 w$ $3w$ and $w (w + 4)$ $w(w+4)$ , whose LCD is $3 w (w + 4)$ $3w(w+4)$

so convertig all to common denomiator, we get

$\frac{3}{w + 4} = \frac{3}{w + 4} \times \frac{3 w}{3 w} = \frac{9 w}{3 w (w + 4)}$ $3/(w+4)=3/(w+4)xx(3w)/(3w)=(9w)/(3w(w+4)$

$\frac{8}{3 w} = \frac{8}{3 w} \times \frac{w + 4}{w + 4} = \frac{8 w + 32}{3 w (w + 4)}$ $8/(3w)=8/(3w)xx(w+4)/(w+4)=(8w+32)/(3w(w+4)$ and

$\frac{12}{w (w + 4)} = \frac{12}{w (w + 4)} \times \frac{3}{3} = \frac{36}{3 w (w + 4)}$ $12/(w(w+4))=12/(w(w+4))xx3/3=36/(3w(w+4)$

Hence, $\frac{3}{w + 4} + \frac{8}{3 w} + \frac{12}{w (w + 4)}$ $3/(w+4)+8/(3w)+12/(w(w+4))$

= $\frac{9 w + 8 w + 32 + 36}{3 w (w + 4)}$ $(9w+8w+32+36)/(3w(w+4)$

= $\frac{17 w + 68}{3 w (w + 4)}$ $(17w+68)/(3w(w+4)$

= $\frac{17 (w + 4)}{3 w (w + 4)}$ $(17(w+4))/(3w(w+4))$

= $(17cancel((w+4)))/(3wcancel((w+4)))$

= $17/(3w)$

How do you simplify 3/(w + 4) + 8/(3w) + 12/(w(w +4))3w+4+83w+12w(w+4)3/(w + 4) + 8/(3w) + 12/(w(w +4))?