<s>[INST] How to find LCM of this equation? Can $(x+1)(2x-1)$ be the LCM of this biquadratic equation 
$$\frac{5x-1}{x+7}=\frac{3x+1}{x+5}$$
 [/INST] The lowest common denominator (LCD) of rational fractions 
$$\frac{5x-1}{x+7}\quad {\rm and} \quad \frac{3x+1}{x+5}$$
is the lowest common multiple (LCM) of denominator polynomials
$$ x+7 \quad {\rm and} \quad x+5, $$
which is 
$$ (x+7)(x+5).$$
So, formally, the original equality of rational fractions can be re-written as:
$$\frac{(5x-1)(x+5)}{(x+7)(x+5)}= \frac{(3x+1)(x+7)}{(x+5)(x+7)}.$$
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