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Here is the problem: 2/(x plus 1) plus 1 equals 3/(x plus 1).

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A quadratic equation in x: solve with the quadratic formula.

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Start with the equation.

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Multiply both sides by x ^ 2 +2 cdot x plus 1 to clear the fractions. This is only valid where x ^ 2 plus 2 times x plus 1 not equal to 0, so any value that makes it zero is excluded at the end.

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Move every term to one side to get standard form.

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Compute the discriminant.

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delta greater than 0, so there are two distinct real roots.

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Apply the quadratic formula.

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Simplify each root.

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Factored form.

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Remove extraneous roots. x equals negative 1 makes a denominator zero and is rejected.

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Now look at the graph of the left side minus the right side.

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It crosses zero exactly at the solutions we found.

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So the answer is x equals 0.

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The quadratic formula gives every solution of ax squared plus bx plus c equals 0.

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x equals 0: left side equals 3, right side equals 3, which checks out.