Question

how do you solve 3/2x-2 + 1/2 = 2/x-1

Answer 1

\[\frac{3}{2x}-2+\frac{1}{2} = \frac{2}{x}-1\]
Is this the problem?

Answer 2

the minus 2 & 1 go with the 2x & x

Answer 3

\[\frac{3}{2x-2}+\frac{1}{2} = \frac{2}{x-1}\]
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Answer 4

okaaaay . how do you do it now

Answer 5

gotcha, first things first, multiply everything by 2 to make it a little nicer to look at this should give you:

3/(x-1) +2 = 4/(x-1)

Answer 6

from here you can notice that we can write the 3/(x-1) and the 4/(x-1) as

3(1/(x-1)) and 4(1/(x-1))

Answer 7

since these are like terms you can add them together.

Answer 8

subtracting 3(1/(x-1)) from each side, you should get:

2=1/(x-1)

Answer 9

now multiply each side by (x-1) to take care of the denominator and get:

2x-2 = 1

Answer 10

add the 2 to each side:

2x = 3

and divide by 2

x= 3/2

Answer 11

Combine the two fractions on the left side by multiplying the top and bottom of the (1/2) by (x-1) so they have a common denominator:\[\frac{3+(x-1)}{2x-2} = \frac{2}{x-1}\]Then cross multiply and arrange the equation so it is equal to zero because it will be a polynomial:\[(x-1)(3+x-1) = 2(2x-2)\]\[x^{2}-3x+2=0\]Then factor and solve for zero:\[(x-2)(x-1) = 0\]So x must equal 2 or 1.