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

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Answer 1 · 2018-06-25T21:29:52

#x=5/11#

Let's subtract #2# from both sides to get

#2/3-6/3=-(5x-3)/(x-1)#

#=>-4/3=-(5x-3)/(x-1)#

To get rid of the #x-1# in the denominator, let's multiply both sides by it. This gives us

#(-4(x-1))/3=-(5x-3)#

We can also get rid of the #3# in the denominator by multiplying both sides by it. We get

#-4(x-1)=-3(5x-3)#

Let's distribute the #-4# and #-3# to their respective terms to get

#-4x+4=-15x+9#

Adding #15x# on both sides gives us

#11x+4=9#

Subtracting #4# from both sides, we get

#11x=5#

Lastly, dividing both sides by #11# gives us

#x=5/11#

Hope this helps!