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

Question

Nathan Axel · Accepted Answer

#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#

I hope this is useful.

Eva Adamson · Answer

undefined To solve the equation 2/3 = 2 - (5x-3)/(x-1), we can start by multiplying both sides of the equation by the common denominator, which is (x-1). This will help us eliminate the fractions.

First, multiply 2/3 by (x-1):

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

Next, simplify both sides of the equation:

2(x-1) = 2(x-1) - (5x-3)

Expand the equation:

2x - 2 = 2x - 2 - 5x + 3

Combine like terms:

2x - 2 = -3x + 1

Move all the variables to one side of the equation:

2x + 3x = 1 + 2

Combine like terms:

5x = 3

Divide both sides of the equation by 5:

x = 3/5

Therefore, the solution to the equation 2/3 = 2 - (5x-3)/(x-1) is x = 3/5.