Solved example of rational equations
Inverting the equation
Apply fraction cross-multiplication
Solve the product $3\left(x+1\right)$
Any expression multiplied by $1$ is equal to itself
Solve the product $3\left(x+1\right)$
Solve the product $2\left(x-1\right)$
Solve the product $3\left(x+1\right)$
Any expression multiplied by $1$ is equal to itself
Multiply $2$ times $-1$
Solve the product $2\left(x-1\right)$
Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side
Subtract the values $-2$ and $-3$
Combining like terms $3x$ and $-2x$
Verify that the solutions obtained are valid in the initial equation
The valid solutions to the equation are the ones that, when replaced in the original equation, don't make any denominator equal to $0$, since division by zero is not allowed
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