What is expand (-16/5)/(t+3)+(11/5)/(t-2) ?

The solution to expand (-16/5)/(t+3)+(11/5)/(t-2) is -(t-13)/(t^2+t-6)

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expand (-16/5)/(t+3)+(11/5)/(t-2)

expand

\frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

- \frac{t - 13}{t ^{2} + t - 6}

Solution steps

\frac{- \frac{16}{5}}{t + 3} + \frac{\frac{11}{5}}{t - 2}

\frac{- \frac{16}{5}}{t + 3} = - \frac{16}{5 t + 15}

= - \frac{16}{5 t + 15} + \frac{\frac{11}{5}}{t - 2}

\frac{\frac{11}{5}}{t - 2} = \frac{11}{5 t - 10}

= - \frac{16}{5 t + 15} + \frac{11}{5 t - 10}

Factor

5 t + 15 : 5 (t + 3)

= - \frac{16}{5 ( t + 3 )} + \frac{11}{5 t - 10}

Factor

5 t - 10 : 5 (t - 2)

= - \frac{16}{5 ( t + 3 )} + \frac{11}{5 ( t - 2 )}

Least Common Multiplier of

5 (t + 3), 5 (t - 2) : 5 (t + 3) (t - 2)

Adjust Fractions based on the LCM

= - \frac{16 ( t - 2 )}{5 ( t + 3 ) ( t - 2 )} + \frac{11 ( t + 3 )}{5 ( t - 2 ) ( t + 3 )}

Since the denominators are equal, combine the fractions:

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

= \frac{- 16 ( t - 2 ) + 11 ( t + 3 )}{5 ( t + 3 ) ( t - 2 )}

Factor

11 (t + 3) - 16 (t - 2) : - 5 (t - 13)

= - \frac{5 ( t - 13 )}{5 ( t + 3 ) ( t - 2 )}

Divide the numbers:

\frac{5}{5} = 1

= - \frac{t - 13}{( t + 3 ) ( t - 2 )}

Expand

(t + 3) (t - 2) : t^{2} + t - 6

= - \frac{t - 13}{t ^{2} + t - 6}

(2 d + e + 5 t) (e + 3 t)

\frac{a ^{3} + b ^{3} + c ^{3}}{( a + b ) ( a + c ) ( b + c )}

\frac{x ^{3} ( 3 a x - 4 a ) - 2 ( b x ^{2} + a x - 1 )}{3 x ^{2} + 2 x - 3}

\frac{( p - 1 )}{p ^{2} ( p ^{2} - 2 p + 5 )}

\frac{( y + 1 ) ^{2}}{y}

What is expand (-16/5)/(t+3)+(11/5)/(t-2) ?
The solution to expand (-16/5)/(t+3)+(11/5)/(t-2) is -(t-13)/(t^2+t-6)