What is (3k-27)/(k^2-8k-9)+(7k+14)/(3k^2+9k+6) ?

The solution to (3k-27)/(k^2-8k-9)+(7k+14)/(3k^2+9k+6) is (16)/(3(k+1))

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simplify (3k-27)/(k^2-8k-9)+(7k+14)/(3k^2+9k+6)

simplify

\frac{3 k - 27}{k ^{2} - 8 k - 9} + \frac{7 k + 14}{3 k ^{2} + 9 k + 6}

\frac{16}{3 ( k + 1 )}

Solution steps

\frac{3 k - 27}{k ^{2} - 8 k - 9} + \frac{7 k + 14}{3 k ^{2} + 9 k + 6}

Cancel

\frac{3 k - 27}{k ^{2} - 8 k - 9} : \frac{3}{k + 1}

= \frac{3}{k + 1} + \frac{7 k + 14}{3 k ^{2} + 9 k + 6}

Cancel

\frac{7 k + 14}{3 k ^{2} + 9 k + 6} : \frac{7}{3 ( k + 1 )}

= \frac{3}{k + 1} + \frac{7}{3 ( k + 1 )}

Least Common Multiplier of

k + 1, 3 (k + 1) : 3 (k + 1)

Adjust Fractions based on the LCM

= \frac{9}{3 ( k + 1 )} + \frac{7}{3 ( k + 1 )}

Apply the fraction rule:

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

= \frac{9 + 7}{3 ( k + 1 )}

Add the numbers:

9 + 7 = 16

= \frac{16}{3 ( k + 1 )}

3 x^{2} - 2 x + 4 = 3 ((x - \frac{1}{3}) + \frac{11}{9})

5 x 1 0^{- 2}

- 3 x + 5 > 17

x^{2} + 14 x + 13

5 x^{2} - 8 x = - 3

What is (3k-27)/(k^2-8k-9)+(7k+14)/(3k^2+9k+6) ?
The solution to (3k-27)/(k^2-8k-9)+(7k+14)/(3k^2+9k+6) is (16)/(3(k+1))