WEBVTT

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Here is the problem: x/(x plus 8) plus 7/(x plus 5) equals 1.

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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 +13 cdot x plus 40 to clear the fractions. This is only valid where x ^ 2 plus 13 times x plus 40 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 16.

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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 16: left side equals 1, right side equals 1, which checks out.