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# Solve the equation 2/(x-1)+1=(4-2x)/(x-1)

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No solution

## Step by step solution

Problem

$\frac{2}{x-1}+1=\frac{4-2x}{x-1}$
1

Grouping terms

$-\frac{4-2x}{x-1}+1+\frac{2}{x-1}=0$
2

Add fraction's numerators with common denominators: $\frac{2}{x-1}$ and $\frac{4-2x}{x-1}$

$1+\frac{2-\left(4-2x\right)}{x-1}=0$
3

Multiplying polynomials $-1$ and $4+-2x$

$1+\frac{2+2x-4}{x-1}=0$
4

Subtract the values $2$ and $-4$

$1+\frac{2x-2}{x-1}=0$
5

Subtract $1$ from both sides of the equation

$\frac{2x-2}{x-1}=-1$
6

Multiply both sides of the equation by $x-1$

$2x-2=-\left(x-1\right)$
7

Multiply $\left(x+-1\right)$ by $-1$

$2x-2=1-x$
8

Grouping terms

$x+2x-2=1$
9

Adding $2x$ and $x$

$3x-2=1$
10

Subtract $-2$ from both sides of the equation

$3x=2+1$
11

Add the values $1$ and $2$

$3x=3$
12

Multiply both sides of the equation by 

$x=1$
13

Since the equation is undefined for $1$

No solution

## Answer

No solution

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