What is expand aln((am)/((a+b)t))+bln((bm)/((a+b)t)) ?

The solution to expand aln((am)/((a+b)t))+bln((bm)/((a+b)t)) is aln((am)/(at+bt))+bln((mb)/(at+bt))

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expand aln((am)/((a+b)t))+bln((bm)/((a+b)t))

expand

a ln (\frac{am}{( a + b ) t}) + b ln (\frac{bm}{( a + b ) t})

a ln (\frac{am}{a t + b t}) + b ln (\frac{mb}{a t + b t})

Solution steps

a ln (\frac{am}{( a + b ) t}) + b ln (\frac{bm}{( a + b ) t})

\frac{am}{( a + b ) t} = \frac{am}{a t + b t}

= a ln (\frac{am}{a t + b t}) + b ln (\frac{mb}{t ( a + b )})

\frac{bm}{( a + b ) t} = \frac{mb}{a t + b t}

= a ln (\frac{am}{a t + b t}) + b ln (\frac{mb}{a t + b t})

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\frac{1}{s ^{4} ( s ^{2} + 1 )}

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\frac{( x + 1 ) ( x )}{2}

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What is expand aln((am)/((a+b)t))+bln((bm)/((a+b)t)) ?
The solution to expand aln((am)/((a+b)t))+bln((bm)/((a+b)t)) is aln((am)/(at+bt))+bln((mb)/(at+bt))