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?
I don't understand the rest
so multipy both sides by
(t-8)(t+7)
(t-24) + 7(t+7)=3(t-8)
solve for t.
The choices are:
a.)-97/5
b.)122/5
c.)-13
d.)-13/5
One of them is correct.
a.)-97/5 is the answer I get is that correct?
Well you had an error in your last equation, which should read
(t+24) + 7(t+7) = 3(t-8)
which becomes
5t = -97
so your answer is correct anyway. You made two cancelling mistakes, or a typing error.
Thank You. I understand.
Your initial step of factoring the denominator is correct. The equation can be rewritten as follows:
(t+24)/(t-8)(t+7) + 7/(t-8) = 3/(t+7)
Now, to simplify the equation further, let's multiply both sides by the common denominator (t-8)(t+7):
[(t-8)(t+7)][(t+24)/(t-8)(t+7)] + [(t-8)(t+7)][7/(t-8)] = [(t-8)(t+7)][3/(t+7)]
Simplifying each part of the equation:
(t+24) + 7(t+7) = 3(t-8)
Expanding:
t + 24 + 7t + 49 = 3t - 24
Combining like terms:
8t + 73 = 3t - 24
Bringing the terms with t to one side:
8t - 3t = -24 - 73
5t = -97
Dividing both sides by 5:
t = -97/5
Therefore, the correct answer is option a.) -97/5.