What is (3n)/(n+3)+5/(n-4) ?

The solution to (3n)/(n+3)+5/(n-4) is (3n^2-7n+15)/((n+3)(n-4))

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simplify (3n)/(n+3)+5/(n-4)

simplify

\frac{3 n}{n + 3} + \frac{5}{n - 4}

\frac{3 n ^{2} - 7 n + 15}{( n + 3 ) ( n - 4 )}

Solution steps

\frac{3 n}{n + 3} + \frac{5}{n - 4}

Least Common Multiplier of

n + 3, n - 4 : (n + 3) (n - 4)

Adjust Fractions based on the LCM

= \frac{3 n ( n - 4 )}{( n + 3 ) ( n - 4 )} + \frac{5 ( n + 3 )}{( n + 3 ) ( n - 4 )}

Apply the fraction rule:

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

= \frac{3 n ( n - 4 ) + 5 ( n + 3 )}{( n + 3 ) ( n - 4 )}

Simplify

3 n (n - 4) + 5 (n + 3) : 3 n^{2} - 7 n + 15

= \frac{3 n ^{2} - 7 n + 15}{( n + 3 ) ( n - 4 )}

\frac{11 - 2}{11 + 2}

\frac{1 + sin ( x )}{cos ( x )}

(2 cos (2 x))^{2}

16 x^{2} - 4 x - 6

\frac{1}{2} + \frac{2}{17}

What is (3n)/(n+3)+5/(n-4) ?
The solution to (3n)/(n+3)+5/(n-4) is (3n^2-7n+15)/((n+3)(n-4))