document.write( "Question 831255: find values of x, satisfying given conditions:\r
\n" ); document.write( "\n" ); document.write( "y(first)=2x/(x+3); y(second)=3/(x+5) , and y(first)+y(second)=1\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #501407 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm changing y(first) to $\"y\"$ and y(second) to $\"z\"$ just for clarity.
\n" ); document.write( "1. $\"y=2x%2F%28x%2B3%29\"$
\n" ); document.write( "2. $\"z=3%2F%28x%2B5%29\"$
\n" ); document.write( "3. $\"y%2Bz=1\"$
\n" ); document.write( "From eq. 3, substitute using eq. 1 and eq. 2,
\n" ); document.write( " $\"2x%2F%28x%2B3%29%2B3%2F%28x%2B5%29=1\"$
\n" ); document.write( " $\"2x%28x%2B5%29%2B3%28x%2B3%29=%28x%2B3%29%28x%2B5%29\"$
\n" ); document.write( " $\"2x%5E2%2B10x%2B3x%2B9=x%5E2%2B8x%2B15\"$
\n" ); document.write( " $\"2x%5E2%2B13x%2B9=x%5E2%2B8x%2B15\"$
\n" ); document.write( " $\"x%5E2%2B5x-6=0\"$
\n" ); document.write( " $\"%28x%2B6%29%28x-1%29=0\"$
\n" ); document.write( "To possible solutions:
\n" ); document.write( " $\"x%2B6=0\"$
\n" ); document.write( " $\"x=-6\"$
\n" ); document.write( "Check the original equation:
\n" ); document.write( " $\"y=2%28-6%29%2F%28-6%2B3%29=-12%2F-3=4\"$
\n" ); document.write( " $\"z=3%2F%28-6%2B5%29=3%2F%28-1%29=-3\"$
\n" ); document.write( " $\"y%2Bz=1\"$
\n" ); document.write( "True
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"x-1=0\"$
\n" ); document.write( " $\"x=1\"$
\n" ); document.write( "Check the original equation:
\n" ); document.write( " $\"y=2%281%29%2F%281%2B3%29=2%2F4=1%2F2\"$
\n" ); document.write( " $\"z=3%2F%281%2B5%29=3%2F6=1%2F2\"$
\n" ); document.write( " $\"y%2Bz=1\"$
\n" ); document.write( "True
\n" ); document.write( "(x,y,z)=(-6,4,-3)
\n" ); document.write( "(x,y,z)=(1,1/2,1/2) \n" ); document.write( "

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