document.write( "Question 1055130: 1/[1+1/(1-1/x)]=2 \n" ); document.write( "

Algebra.Com's Answer #846786 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Solve by simplifying the expression on the left using basic rules of algebra, starting with the innermost parentheses and working out.

\n" ); document.write( " $\"1-1%2Fx=x%2Fx-1%2Fx=%28x-1%29%2Fx\"$

\n" ); document.write( " $\"1%2F%28%28x-1%29%2Fx%29=x%2F%28x-1%29\"$

\n" ); document.write( " $\"1%2Bx%2F%28x-1%29=%28x-1%29%2F%28x-1%29%2Bx%2F%28x-1%29=%282x-1%29%2F%28x-1%29\"$

\n" ); document.write( " $\"1%2F%28%282x-1%29%2F%28x-1%29%29=%28x-1%29%2F%282x-1%29\"$

\n" ); document.write( "Now we are ready to write and solve the equation using this simplified form of the expression.

\n" ); document.write( " $\"%28x-1%29%2F%282x-1%29=2\"$
\n" ); document.write( " $\"2%282x-1%29=x-1\"$
\n" ); document.write( " $\"4x-2=x-1\"$
\n" ); document.write( " $\"3x=1\"$
\n" ); document.write( " $\"x=1%2F3\"$

\n" ); document.write( "ANSWER: 1/3

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