## anonymous 4 years ago If a, b are the solutions of (((15)/(t+6))+((t+4)/(3)))=4 compute the sum of a+b plz show work and i would be very happy if someone were to help me/explain this problem

1. anonymous

first let me see if i can read what is says

2. anonymous

$\frac{15}{t+6}+\frac{t+4}{3}=4$??

3. anonymous

yuppers

4. anonymous

the sum of a+b for tht equation

5. anonymous

well i don't think there is a shortcut. i think you have to find the solutions and add them

6. anonymous

or at least write the quadratic equation out

7. anonymous

oh damn i made a mistake!

8. anonymous

$\frac{45+(t+4)(t+6)}{3(t+6)}=4$

9. anonymous

$45+(t+4)(t+6)=12(t+6)$ $t^2+10t+69=12t+72$ $t^2-2t-3=0$ and finally $(t-3)(t+1)=0$ solutions area 3 and -1

10. anonymous

if you add them you get 2

11. anonymous

it is also true that the sum of the solutions to $ax^2+bx+c=0$ is $-\frac{b}{a}$so we did not actually have to solve once we got to $x^2-2x-3=0$

12. anonymous

thank much man appreciate it hope some good karma comes back to u one day ^^