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

Guest Feb 11, 2018

#1**0 **

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**

Guest Feb 11, 2018