# How do you solve #3/(x-3)=x/(x-3)-3/2#?

##### 2 Answers

There are no solutions.

#### Explanation:

put the RHS over a common denominator

that gives us

cross multiply to make it a linear problem (no fractions)

collect all terms onto one side

Factorise

so

If

The graph of

Thanks @georgec for the update.

There is no value of

#### Explanation:

Given:

#3/(x-3) = x/(x-3)-3/2#

Adding

#3/2 = (x-3)/(x-3) = 1" "(x != 3)#

Since this is false, there is no value of

Here are the graphs of the left hand side and right hand side of the given equation plotted together:

graph{(y-3/(x-3))(y - (x/(x-3)-3/2)) = 0 [-10, 10, -5, 5]}

The two hyperbolas do not intersect, but have a common vertical asymptote at