WEBVTT

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

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A linear equation in x: isolate x using inverse operations.

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Start with the equation.

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Multiply both sides by x ^ 2 -3 cdot x plus 2 to clear the fractions. This is only valid where x ^ 2 minus 3 times x plus 2 not equal to 0, so any value that makes it zero is excluded at the end.

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Isolate x.

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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 5.

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Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

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x equals 5: left side equals 2, right side equals 2, which checks out.