How do you solve 1/2(x-3)+3/(2-x)=5 x?

1 Answer
Jul 10, 2016

The soln. set is {0,5/3}.

Explanation:

1/2*(x-3)+3/(2-x)=5x.

:. {(x-3)(2-x)+3*2}/(2(2-x))=5x.

:. (x-3)(2-x)+6=10x(2-x).

:. (x-3)(2-x)-10x(2-x)+6=0.

:. (2-x){x-3-10x}+6=0.

:.(2-x)(-9x-3)+6=0.

:.(x-2)(9x+3)+6=0.

:. 9x^2-18x+3x-6+6=0.

:. 9x^2-15x=0.

:. 3x(3x-5)=0.

:. x=0, or, x=5/3.

We can easily verify that these roots satisfy the given eqn. Therefore,

The soln. set is {0,5/3}.