How do you add $\frac{12 y}{y^{2} + 16 y + 48} + \frac{6}{y + 4}$ $\frac { 12y } { y ^ { 2} + 16y + 48} + \frac { 6} { y + 4}$ ?

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How do you add $\frac{12 y}{y^{2} + 16 y + 48} + \frac{6}{y + 4}$ $\frac { 12y } { y ^ { 2} + 16y + 48} + \frac { 6} { y + 4}$ ?

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Answer 1 · 2017-02-02T19:55:37

$\frac{6 (y + 14)}{(y + 4) (y + 12)}$ $(6(y+14))/((y+4)(y+12))$

Explanation:

$\frac{12}{y^{2} + 16 y + 48} + \frac{6}{y + 4}$ $12/(y^2+16y+48)+6/(y+4)$
Factorise
$\frac{12}{(y + 4) (y + 12)} + \frac{6}{y + 4}$ $12/((y+4)(y+12))+6/(y+4)$

So to get a common denominator multiply numerator and denominator of the second term by y+12

$= \frac{12}{(y + 4) (y + 12)} + \frac{6}{y + 4} \cdot \frac{y + 12}{y + 12}$ $=12/((y+4)(y+12))+6/(y+4)*(y+12)/(y+12)$

$= \frac{12 + 6 (y + 12)}{(y + 4) (y + 12)}$ $=(12+6(y+12))/((y+4)(y+12))$
$= \frac{12 + 6 y + 72}{(y + 4) (y + 12)}$ $=(12+6y+72)/((y+4)(y+12))$
$= \frac{6 y + 84}{(y + 4) (y + 12)}$ $=(6y+84)/((y+4)(y+12))$
$= \frac{6 (y + 14)}{(y + 4) (y + 12)}$ $=(6(y+14))/((y+4)(y+12))$

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How do you add $\frac{12 y}{y^{2} + 16 y + 48} + \frac{6}{y + 4}$ $\frac { 12y } { y ^ { 2} + 16y + 48} + \frac { 6} { y + 4}$ ?

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How do you add 12yy2+16y+48+6y+4\frac { 12y } { y ^ { 2} + 16y + 48} + \frac { 6} { y + 4}?

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How do you add $\frac{12 y}{y^{2} + 16 y + 48} + \frac{6}{y + 4}$ $\frac { 12y } { y ^ { 2} + 16y + 48} + \frac { 6} { y + 4}$ ?