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Given $\displaystyle \frac{3a+2b}{a}=\frac{2a+5b}{c}=\frac{5c-2b}{b}$, find $\dfrac{2a-3b}{a+b}$.

I couln't manipulate.

1 Answers 1

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HINT:

Assuming $a+b+c\ne0,$

$$\frac{3a+2b}{a}=\frac{2a+5b}{c}=\frac{5c-2b}{b}=\dfrac{3a+2b+2a+5b+5c-2b}{a+b+c}=?$$

Express $c,b$ in terms of $a$

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    Maybe, it should be recalled the following rule alas no longer taught in schools (for long now, at least in my country): $A/B=C/D \implies A/B=C/D=(aA+bB)/(aC+bD)$ for any $a,b$ (as long as the last denominator is not zero...) – 2017-01-19
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    I got it, thanks. – 2017-01-29