Solve equation t/t-3 + 2 = 3/t-3?

Question

How to solve this equation.

Answer 1

Gather like terms and solve for t,

t/(t-3)-3/(t-3)=-2

(t-3)/(t-3)=-2

since -1<>-2

there is no solution....

Answer 2

first, cross multiply

so you get t^2-3t = 3t-9+6

then bring everything to one side

t^2-6t+3 = 0

... ok i'm lost, have you learned the quadratic formula?

EDIT:  ooooh ok i you should've clarified by doing

(t/t-3) + 2 = 3/t-3.  that confused me :P  well someone already answered correctly, so i'm not even gonna bother

Answer 3

Multiply all the equation by t-3

this gives:

                                     t+2t-6=3

                                    

                                    3t=9

                                      t=3

Answer 4

Multiply both sides by (t-3).  This gets rid of the fractions, and makes it easier to solve for t.

t + 2(t-3) = 3

3t - 6 = 3

3t = 9

t = 3.

It would seem that this is the solution, but hold on.  When we multiplied both sides by t-3, we basically ended up multiplying both sides by 0.  You can take 1 = 5 and multiply both sides by 0 to get 0=0, but that doesn't mean 1=5 is true.  If you put t = 3 back into the original equation, then you end up dividing by 0.  So there's no solution.

Answer 5

Start by multiplying everything by (t-3):

t/(t - 3) + 2 = 3/(t - 3)

t + 2(t - 3) = 3

t + 2t - 6 = 3

3t = 9

t = 3

But since you had (t - 3) in the denominator of the equation, if t = 3, you'd be dividing by zero, so t = 3 isn't a possible answer.

So there is no solution to the given problem.