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

The solution to expand-(-16/5)/(t+3)+(11/5)/(t-2) is (27t+1)/(5t^2+5t-30)

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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{27 t + 1}{5 t ^{2} + 5 t - 30}

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

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

Apply rule

- (- a) = a

= \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 )}

Expand

5 (t + 3) (t - 2) : 5 t^{2} + 5 t - 30

= \frac{16 ( t - 2 ) + 11 ( t + 3 )}{5 t ^{2} + 5 t - 30}

Expand

16 (t - 2) + 11 (t + 3) : 27 t + 1

= \frac{27 t + 1}{5 t ^{2} + 5 t - 30}

\frac{n ( n + 1 ) ( n + 2 ) ( n + 3 )}{4}

\frac{40960000}{( 4096 - x ) ^{2}}

(e^{t} - 3)^{2}

\frac{d}{d x} ((100 - 2 x) \cdot x) - x^{2}

\frac{x ^{2} + x - 1}{( x ^{2} + 1 ) ^{2}}

What is expand-(-16/5)/(t+3)+(11/5)/(t-2) ?
The solution to expand-(-16/5)/(t+3)+(11/5)/(t-2) is (27t+1)/(5t^2+5t-30)