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

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Answer 1 · 2016-07-10T07:03:43

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

#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}.#