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\frac{\frac{bb}{bc}-\frac{cc}{bc}}{\frac{b-c}{2bc}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c and b is bc. Multiply \frac{b}{c} times \frac{b}{b}. Multiply \frac{c}{b} times \frac{c}{c}.
\frac{\frac{bb-cc}{bc}}{\frac{b-c}{2bc}}
Since \frac{bb}{bc} and \frac{cc}{bc} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{b^{2}-c^{2}}{bc}}{\frac{b-c}{2bc}}
Do the multiplications in bb-cc.
\frac{\left(b^{2}-c^{2}\right)\times 2bc}{bc\left(b-c\right)}
Divide \frac{b^{2}-c^{2}}{bc} by \frac{b-c}{2bc} by multiplying \frac{b^{2}-c^{2}}{bc} by the reciprocal of \frac{b-c}{2bc}.
\frac{2\left(b^{2}-c^{2}\right)}{b-c}
Cancel out bc in both numerator and denominator.
\frac{2\left(b+c\right)\left(b-c\right)}{b-c}
Factor the expressions that are not already factored.
2\left(b+c\right)
Cancel out b-c in both numerator and denominator.
2b+2c
Expand the expression.
\frac{\frac{bb}{bc}-\frac{cc}{bc}}{\frac{b-c}{2bc}}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c and b is bc. Multiply \frac{b}{c} times \frac{b}{b}. Multiply \frac{c}{b} times \frac{c}{c}.
\frac{\frac{bb-cc}{bc}}{\frac{b-c}{2bc}}
Since \frac{bb}{bc} and \frac{cc}{bc} have the same denominator, subtract them by subtracting their numerators.
\frac{\frac{b^{2}-c^{2}}{bc}}{\frac{b-c}{2bc}}
Do the multiplications in bb-cc.
\frac{\left(b^{2}-c^{2}\right)\times 2bc}{bc\left(b-c\right)}
Divide \frac{b^{2}-c^{2}}{bc} by \frac{b-c}{2bc} by multiplying \frac{b^{2}-c^{2}}{bc} by the reciprocal of \frac{b-c}{2bc}.
\frac{2\left(b^{2}-c^{2}\right)}{b-c}
Cancel out bc in both numerator and denominator.
\frac{2\left(b+c\right)\left(b-c\right)}{b-c}
Factor the expressions that are not already factored.
2\left(b+c\right)
Cancel out b-c in both numerator and denominator.
2b+2c
Expand the expression.