I don't know what to do to derive the right side from the left side: $$\frac{B}{1+r} = B - \frac{r B}{1+r}.$$
Which steps I have to do to get this equation?
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algebra-precalculus
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1Instead, derive the left side from the right side (with a least common denominator), then work backwards. – 2011-07-05
2 Answers
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Hint: Write the numerator of the left hand side as $B(1+r-r)$ and use the fact that $$\frac{a+c}{d}=\frac{a}{d}+\frac{c}{d}$$ for $d\neq 0.$
Added:
Observe that $\,\,$ $B=B(1+r-r)=B(1+r)-rB.$
So $$
\begin{align*}\frac{B}{1+r}&=\frac{B(1+r)-rB}{1+r}\\
&= \frac{B(1+r)}{1+r}-\frac{rB}{1+r}\\
&= B-\frac{rB}{1+r}.
\end{align*}$$
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0Could you please show the whole transformation? – 2011-07-05
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0@Georg: I have added to my answer. – 2011-07-05
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0Great, thanks a lot! – 2011-07-05
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HINT $\ $ It's simply $\rm\displaystyle\ 1\ =\ \frac{1+r}{1+r}\ =\ \frac{1}{1+r}\ +\ \frac{r}{1+r}\ $ rearranged, then scaled by $\rm\:B\:.$