Question

1)Find the LCM of m^2-4m-5 and m^2+8m+7.

factorize both expressions you get
(m+1)(m-5)
and
(m+1)(m+7)

common factor is m+1
so LCM =
(m+1)(m-5)(m+7) = m^3+3m^2-33m-35

2)Solve 8/(t+5)=(t-3)/(t+5)+(1/3).

First convert the 1/3 to a fraction with (t+5) on the bottom and the other two terms to have a 3*(t+5) on the bottom:

[8 * 3 / (t+5) * 3] = [(t-3) * 3 / (t+5) * 3] + 1/3 * (t+5)/(t+5)
[8 * 3 / (t+5) * 3] = [(t-3) * 3 / (t+5) * 3] + (t+5)/[(t+5) * 3]

Then multiply both sides by (t+5) * 3:

8 * 3 = (3t -9) + (t + 5)
24 = 3t + t - 9 + 5
24 = 4t - 4
24 + 4 = 4t - 4 + 4
28 = 4t
4t / 4 = 28 / 4
t = 7