Question:
If $fraction numerator a space plus b x over denominator a space minus space b x end fraction space equals space fraction numerator b space plus space c x over denominator b space minus space c x end fraction space equals space fraction numerator c space plus space d x over denominator c space minus d x end fraction space open parentheses x space not equal to 0 close parentheses$ Answer:

It is given that,

$fraction numerator a space plus space b x over denominator a space minus b x end fraction space equals space fraction numerator b space plus space c x over denominator b space minus c x end fraction rightwards double arrow space open parentheses a space plus space b x close parentheses open parentheses b minus c x close parentheses space equals space open parentheses b plus c x close parentheses open parentheses a minus b x close parentheses rightwards double arrow a b space minus space a c x space plus space b squared x space minus space b c x squared space equals space a b space minus space b squared x space plus space a c x space minus space b c x squared rightwards double arrow 2 b squared x space equals space 2 a c x rightwards double arrow b squared space equals space a c rightwards double arrow b over a space equals space c over b space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis A l s o comma space fraction numerator b plus c x over denominator b minus c x end fraction space equals space fraction numerator c space plus d x over denominator c space minus d x end fraction space rightwards double arrow open parentheses b plus c x close parentheses open parentheses c minus d x close parentheses space equals space open parentheses b minus c x close parentheses open parentheses c plus d x close parentheses rightwards double arrow b c space minus space b d x space plus space c squared x space minus space c d x squared space equals space b c space plus space b d x space minus space c squared x space minus space c d x squared rightwards double arrow 2 c squared x space equals space 2 b d x rightwards double arrow c squared space equals space b d rightwards double arrow c over d space equals space d over c space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis$

From (1) and (2), we obtain

$b over a space equals space c over b space equals d over c$

Thus, a, b, c, and d are in G.P.

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Question: If Answer: It is given that, From (1) and (2), we obtain Thus, a, b, c, and d are in G.P.

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