How do you solve #\frac { 1} { x - 3} = \frac { 3} { x } - \frac { 3} { x - 3}#?

1 Answer
graces
May 6, 2017

First you need to get a common denominator. In this case it would be #x^2 -3x#.

Explanation:

To get the term 1/(x-3) to have the common denominator, you need to multiply the numerator and the denominator by x. To get the term 3/x to have the common denominator, multiply the numerator and the denominator by x-3. To get the term 3/(x-3) to have the common denominator, multiply the numerator and the denominator by x.
Then you end up with:
#x/(x^2 -3x) = [(3x-9)/(x^2 -3x)] - [(3x)/(x^2 -3x)]#

Next, combine the two terms on the right of the equals sign.
You end up with:
#x/(x^2 -3x) = -9/(x^2 -3x)#

Then you have to multiply the entire equation by #x^2 -3x#, so you can get rid of the denominator by cancelling.
#x^2 -3x*[x/(x^2 -3x) = -9/(x^2 -3x)]#

#x=-9#
Hope this helps :)

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