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
To solve this equation step-by-step, we start with the equation:
8/(t+5) = (t-3)/(t+5) + 1/3
First, let's multiply both sides of the equation by (t+5) to get rid of the denominators:
8 * (t+5)/(t+5) = (t-3) * (t+5)/(t+5) + 1/3 * (t+5)/(t+5)
Simplifying both sides gives:
8 = (t-3) + (t+5)/(3)
Next, let's simplify the right side of the equation:
8 = t - 3 + (t+5)/(3)
Now, let's combine like terms:
8 = t + (t-3)/(3) + 5/(3)
To get rid of the fractions, we can multiply both sides of the equation by 3:
8 * 3 = t*3 + (t-3) + 5
Simplifying further gives:
24 = 3t + t - 3 + 5
Combining like terms again:
24 = 4t + 2
Subtracting 2 from both sides:
24 - 2 = 4t
Simplifying:
22 = 4t
Finally, divide both sides by 4 to solve for t:
22/4 = t
Simplifying the division gives:
t = 5.5 or t = 11/2