1 answer

Given #f(x)=x/(x-1)#, how do you find the values of x for which #f(x)=2/3#?

Question:

Given #f(x)=x/(x-1)#, how do you find the values of x for which #f(x)=2/3#?

Answers

#x = -2#

Explanation:

First, we must write this problem as"

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

To solve this we should first multiply this equation by a common denominator to eliminate the fractions and to keep the equation balanced. In this case we can multiply by #3(x - 1)#:

#((3(x - 1))x)/(x - 1) = ((3(x - 1))*2)/3#

#((3cancel((x - 1)))x)/(cancel(x - 1)) = ((cancel(3)(x - 1))*2)/cancel(3)#

#3x = (x - 1)2#

Next, we can expand the term in parenthesis:

#3x = 2x - 2#

Now we can isolate the #x# term on one side of the equation and the constant on the other side of the equation while keeping the equation balanced:

#3x - 2x = 2x -2x - 2#

#3x - 2x = 0 - 2#

Now we can consolidate likes terms to solve for #x#:

#(3 - 2)x = -2#

#1x = -2#

#x = -2#

.

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