WEBVTT

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Here is the problem: x/(x minus 5) plus 5/(x minus 4) 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 -9 cdot x plus 20 to clear the fractions. This is only valid where x ^ 2 minus 9 times x plus 20 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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So the answer is x equals 9 over 2 approximately 4.5.

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