document.write( "Question 1045306: I am a little confused over this so please help me solving it
\n" ); document.write( " $\"a%5Ep=b%5Eq=c%5Er=d%5Es\"$ and ab=cd then the value of $\"1%2Fp%2B1%2Fq-1%2Fr-1%2Fs\"$ reduces to? \n" ); document.write( "

Algebra.Com's Answer #660706 by KMST(5328) $\"\"$ $\"About$

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The expression $\"1%2Fp%2B1%2Fq-1%2Fr-1%2Fs\"$ will be undefined if one or more of those denominators is zero.
\n" ); document.write( "If nothing was specified about the exponents,
\n" ); document.write( "we have to consider the case that one (or more) of them is zero:
\n" ); document.write( "If $\"pqrs=0\"$ , then $\"1%2Fp%2B1%2Fq-1%2Fr-1%2Fs\"$ is undefined.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If $\"pqrs%3C%3E0\"$ , then $\"1%2Fp%2B1%2Fq-1%2Fr-1%2Fs=highlight%280%29\"$ :
\n" ); document.write( "Looking at just $\"c%5Er=d%5Es\"$ , we can write
\n" ); document.write( " $\"c%5Er=d%5Es\"$ ---> $\"%28c%5Er%29%5E%281%2Fr%29=%28d%5Es%29%5E%281%2Fr%29\"$ ---> $\"c%5E%22r%2Fr%22=d%5E%22s%2Fr%22\"$ ---> $\"c=d%5E%22s%2Fr%22\"$ .
\n" ); document.write( "Since $\"a%5Ep=d%5Es\"$ and $\"b%5Eq=d%5Es\"$ ,
\n" ); document.write( "we can also write $\"a\"$ and $\"b\"$ as powers of $\"d\"$ :
\n" ); document.write( " $\"a=d%5E%22s%2Fp%22\"$ and $\"b=d%5E%22s%2Fq%22\"$ .
\n" ); document.write( "Substituting the expressions found for $\"a\"$ , $\"b\"$ , and $\"c\"$ into $\"ab=cd\"$ , we get to the solution.
\n" ); document.write( " $\"a%2Ab=c%2Ad\"$ --> $\"d%5E%22s%2Fp%22%2Ad%5E%22s%2Fq%22=d%5E%22s%2Fr%22%2Ad\"$ --> $\"d%5E%22s%2Fp%22%2Ad%5E%22s%2Fq%22=d%5E%22s%2Fr%22%2Ad\"$ --> $\"d%5E%28%22s%2Fp%22%2B%22s%2Fq%22%29=d%5E%28%22s%2Fr%22%2B1%29\"$ --> $\"s%2Fp%2Bs%2Fq=r%2Fs%2B1\"$
\n" ); document.write( "And multiplkying both sides of the last equation above times $\"1%2Fs\"$ , we get
\n" ); document.write( " $\"1%2Fp%2B1%2Fq=1%2Fr%2B1%2Fs\"$ .
\n" ); document.write( "So, subtracting $\"1%2Fr%2B1%2Fs\"$ from both sides, we get
\n" ); document.write( " $\"1%2Fp%2B1%2Fq-%281%2Fr%2B1%2Fs%29=1%2Fr%2B1%2Fs-%281%2Fr%2B1%2Fs%29\"$ --> $\"1%2Fp%2B1%2Fq-1%2Fr-1%2Fs=1%2Fr%2B1%2Fs-1%2Fr-1%2Fs\"$ --> $\"highlight%281%2Fp%2B1%2Fq-1%2Fr-1%2Fs=0%29\"$ . \n" ); document.write( "

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