Solution 2.1:1d
From Förberedande kurs i matematik 1
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<math>\qquad \frac{x^3y^2}{xy}=\frac{x\cdot x\cdot x \cdot y \cdot y}{x\cdot y} = x\cdot x\cdot y = x^2y </math> | <math>\qquad \frac{x^3y^2}{xy}=\frac{x\cdot x\cdot x \cdot y \cdot y}{x\cdot y} = x\cdot x\cdot y = x^2y </math> | ||
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Revision as of 06:32, 21 August 2008
After \displaystyle x^3y^2 are multiplied inside the bracket, we can eliminate factors which occur in both the numerator and denominator.
\displaystyle \qquad \begin{align} x^3y^2\Big( \frac 1y - \frac 1{xy} +1 \Big) &= x^3y^2 \cdot\frac 1y -x^3y^2 \cdot \frac 1{xy} +x^3y^2\cdot 1 \\ &=\frac{x^3y^2}{y} -\frac{x^3y^2}{xy} +x^3y^2 \\ &=x^3y - x^2y +x^3y^2 \end{align}
where we have used
\displaystyle \qquad \frac{x^3y^2}{y}= \frac{x^3\cdot y\cdot y}{y}= x^3y ,
\displaystyle \qquad \frac{x^3y^2}{xy}=\frac{x\cdot x\cdot x \cdot y \cdot y}{x\cdot y} = x\cdot x\cdot y = x^2y
