Question: Verifying positiveness

Hi,

how can I check in maple if my variable P is positive (always or only for some certain conditions)

P=(exp(a-1)-exp(g-1))*(b*d*(f-g)-b*g*(a-e)-g*(a-c)*(a-e)))/((a-g)*b*d) + exp(g-1)*(((a-c)*(a-e))/b*d + (a-e)/d + 1)

with assumptions

a>0,b>0,c>0,d>0,e>0,f>0,g>0 and a>c,e,g

I need to prove that P is always positive with that assumptions, how?

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