If $b = \frac{2 a}{a - 2}$ and $c = \frac{3 b - 4}{4 b + 3},$ find an expression for $c$ in terms of $a$ and find the coefficient of a in the denominator

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Solution

Given, $c = \frac{3 b - 4}{4 b + 3}$
But, $b = \frac{2 a}{a - 2}$
Hence, $c = \frac{3 (\frac{2 a}{a - 2}) - 4}{4 (\frac{2 a}{a - 2}) + 3}$
$\Rightarrow c = \frac{6 a - 4 a + 8}{8 a + 3 a - 6}$
$\Rightarrow c = \frac{2 a + 8}{11 a - 6}$
$\Rightarrow c = \frac{2 (a + 4)}{11 a - 6}$

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Similar questions

b = \frac{2 a}{a - 2}

c = \frac{3 b - 4}{4 b + 3}

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