Solve:
(t+24)/(t^2-t-56)+7/(t-8)=3/(t+7)
I do know that (t^2-t-56) can be factored out to (t-8)(t+7) so I have the equation as (t+24/(t-8)(t+7) +7(t+7)/(t-8)(t+7)-3(x-8)/(t-8)(t+7) is this correct ot what am I doing wrong?
Assistance needed.
Solve:
(t+24)/(t^2-t-56)+7/(t-8)=3/(t+7)
How do I solve this problem
the common denominator is (t-8)(t+7)
so multipy both sides by
(t-8)(t+7)
(t-24) + 7(t+7)=3(t-8)
solve for t.
You are on the right track! However, there seems to be a mistake in your equation. The third term looks incorrect. It should be 3/(t-8), not 3/(t+8).
Let's rewrite the equation using the common denominator (t-8)(t+7):
(t+24)/(t-8)(t+7) + 7(t+7)/(t-8)(t+7) - 3/(t-8) = 0
To simplify this equation, we need to combine the fractions on the left side:
[(t+24) + 7(t+7) - 3]/(t-8)(t+7) = 0
Now, let's simplify the numerator further:
[t + 24 + 7t + 49 - 3]/(t-8)(t+7) = 0
Combining like terms, we get:
[8t + 70]/(t-8)(t+7) = 0
Now, to solve this equation, we need to set the numerator equal to zero:
8t + 70 = 0
Subtract 70 from both sides:
8t = -70
Divide both sides by 8:
t = -70/8
Simplifying the result:
t = -8.75
So, the solution to the given equation is t = -8.75.