What is 3/(y+3)+(2y)/(y^2+8x+15) ?

The solution to 3/(y+3)+(2y)/(y^2+8x+15) is (5y^2+6y+24x+45)/((y+3)(y^2+8x+15))

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simplify 3/(y+3)+(2y)/(y^2+8x+15)

simplify

\frac{3}{y + 3} + \frac{2 y}{y ^{2} + 8 x + 15}

\frac{5 y ^{2} + 6 y + 24 x + 45}{( y + 3 ) ( y ^{2} + 8 x + 15 )}

Solution steps

\frac{3}{y + 3} + \frac{2 y}{y ^{2} + 8 x + 15}

Least Common Multiplier of

y + 3, y^{2} + 8 x + 15 : (y + 3) (y^{2} + 8 x + 15)

Adjust Fractions based on the LCM

= \frac{3 ( y ^{2} + 8 x + 15 )}{( y + 3 ) ( y ^{2} + 8 x + 15 )} + \frac{2 y ( y + 3 )}{( y + 3 ) ( y ^{2} + 8 x + 15 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{3 ( y ^{2} + 8 x + 15 ) + 2 y ( y + 3 )}{( y + 3 ) ( y ^{2} + 8 x + 15 )}

Simplify

3 (y^{2} + 8 x + 15) + 2 y (y + 3) : 5 y^{2} + 6 y + 24 x + 45

= \frac{5 y ^{2} + 6 y + 24 x + 45}{( y + 3 ) ( y ^{2} + 8 x + 15 )}

1 + \frac{1}{2} + \frac{1}{4}

\frac{7 x}{6} - \frac{3 x}{8}

8 \times 8 \times 8 \times 8

(- 7 x^{4} - 7 x^{2} + 6 x - 8) - (9 x^{4} - 9 + 3 x^{2})

x^{2} + 2 x

What is 3/(y+3)+(2y)/(y^2+8x+15) ?
The solution to 3/(y+3)+(2y)/(y^2+8x+15) is (5y^2+6y+24x+45)/((y+3)(y^2+8x+15))