Questions: x-1=(x^2-4x+3)/(x+2)

Transcript text: $x-1=\frac{x^{2}-4 x+3}{x+2}$

Solution

Solution Steps

To solve the equation $ x - 1 = \frac{x^2 - 4x + 3}{x + 2} $, we need to eliminate the fraction by multiplying both sides by $ x + 2 $. Then, we simplify and solve the resulting quadratic equation.

Step 1: Eliminate the Fraction

We start with the equation

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

To eliminate the fraction, we multiply both sides by $ x + 2 $:

\[ (x - 1)(x + 2) = x^2 - 4x + 3 \]

Step 2: Expand and Rearrange

Expanding the left side gives us:

\[ x^2 + 2x - x - 2 = x^2 - 4x + 3 \]

This simplifies to:

\[ x^2 + x - 2 = x^2 - 4x + 3 \]

Next, we rearrange the equation by moving all terms to one side:

\[ x^2 + x - 2 - x^2 + 4x - 3 = 0 \]

This simplifies to:

\[ 5x - 5 = 0 \]

Step 3: Solve for $ x $

Now, we can solve for $ x $:

\[ 5x = 5 \implies x = 1 \]

Final Answer

The solution to the equation is

\[ \boxed{x = 1} \]

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