You also had a missing bracket in "1/ (a(a+3)" which I assume is "1/ (a(a+3))"
So the expression to simplify is probably 1/(a(a+3)) + 1/((a+3)(a+6)) + 1/((a+6)(a+9)) + 1/((a+9)(a+12)) + 1/((a+12)(a+15))
To start you off...
[math]\frac{1}{a \left(a+3\right)}+\frac{1}{\left(a+3\right)\left(a+6\right)}+\ldots[/math]
[math]\frac{1}{a+3} \left(\frac{1}{a}+\frac{1}{a+6}\right)+\ldots[/math]
[math]\frac{1}{a+3} \left( \frac{a+6+a}{a\left(a+6\right)}\right)+\ldots[/math]
[math]\frac{1}{a+3} \left( \frac{2\left(a+3\right)}{a\left(a+6\right)} \right)+\ldots[/math]
[math]\frac{2}{a \left(a+6\right)}+\ldots[/math]
can you continue with the rest of your expression?
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