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Find all values of $t$ that satisfy $\dfrac{t+4}{t+5} = \dfrac{t-5}{2t}$.

 Feb 11, 2018
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Solve for t:

(t + 4)/(t + 5) = (t - 5)/(2 t)

 

Cross multiply:

2 t (t + 4) = (t - 5) (t + 5)

 

Expand out terms of the left hand side:

2 t^2 + 8 t = (t - 5) (t + 5)

 

Expand out terms of the right hand side:

2 t^2 + 8 t = t^2 - 25

 

Subtract t^2 - 25 from both sides:

t^2 + 8 t + 25 = 0

 

Subtract 25 from both sides:

t^2 + 8 t = -25

 

Add 16 to both sides:

t^2 + 8 t + 16 = -9

 

Write the left hand side as a square:

(t + 4)^2 = -9

 

Take the square root of both sides:

t + 4 = 3 i or t + 4 = -3 i

Subtract 4 from both sides:

t = -4 + 3 i or t + 4 = -3 i

 

Subtract 4 from both sides:

t = -4 + 3 i              or               t = -4 - 3 i

 Feb 11, 2018

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