document.write( "Question 1105252: Solve fractional equation: 6/ x-3 - 5/x+1 = 7/x^2-2x-3 \n" ); document.write( "

Algebra.Com's Answer #720020 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "We know what the equation is supposed to be; it would be nice if you showed it to us correctly. As another tutor here likes to say, \"Parentheses are free. Use them.\"

\n" ); document.write( "Here is the equation you show:
\n" ); document.write( " $\"6%2F+x-3+-+5%2Fx%2B1+=+7%2Fx%5E2-2x-3\"$

\n" ); document.write( "Obviously the equation is supposed to be
\n" ); document.write( " $\"6%2F%28x-3%29+-+5%2F%28x%2B1%29+=+7%2F%28x%5E2-2x-3%29\"$

\n" ); document.write( "The denominator of the fraction on the right is the least common denominator for all three fractions. So multiply both sides of the equation by that least common denominator to clear the fractions.

\n" ); document.write( "

\n" ); document.write( " $\"6%28x%2B1%29+-+5%28x-3%29+=+7\"$
\n" ); document.write( " $\"6x%2B6-5x%2B15+=+7\"$
\n" ); document.write( " $\"x%2B21+=+7\"$
\n" ); document.write( " $\"x+=+-14\"$

\n" ); document.write( "CHECK:

\n" ); document.write( " $\"6%2F%28-14-3%29+-+5%2F%28-14%2B1%29+=+7%2F%28%28-14%29%5E2-2%28-14%29-3%29\"$
\n" ); document.write( " $\"-6%2F17+%2B+5%2F13+=+7%2F221\"$
\n" ); document.write( " $\"-6%2813%29+%2B+5%2817%29+=+7\"$
\n" ); document.write( " $\"-78+%2B+85+=+7\"$
\n" ); document.write( " $\"7+=+7\"$ \n" ); document.write( "

\n" );