Solve a/(b-c) = a/b - a/c

Evaluate

\frac{a}{b - c} = \frac{a}{b} - \frac{a}{c}

Multiply both sides of the equation by LCD

\frac{a}{b - c} \times (b^{2} c - b c^{2}) = (\frac{a}{b} - \frac{a}{c}) (b^{2} c - b c^{2})

Simplify the equation

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b c a = (\frac{a}{b} - \frac{a}{c}) (b^{2} c - b c^{2})

Simplify the equation

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b c a = (b c - c^{2}) a + (- b^{2} + b c) a

Simplify

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b c a = (2 b c - c^{2} - b^{2}) a

Add or subtract both sides

b c a - (2 b c - c^{2} - b^{2}) a = 0

Calculate

b c a + (- 2 b c + c^{2} + b^{2}) a = 0

Simplify

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(- b c + c^{2} + b^{2}) a = 0

Solution

a = 0

Solve the equation