document.write( "Question 231195: This is a rational equation. 4 over X plus 7 equals 2 over 3X \n" ); document.write( "

Algebra.Com's Answer #171147 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"4%2Fx+%2B+7+=+2%2F%283x%29\"$
\n" ); document.write( "Equations are easier without fractions. So let's start be getting rid of the fractions. To get rid of fractions in an (simplified) equation like yours, just multiply both sides of the equation by the Lowest Common Denominator (LCD) of all the denominators (on both sides of the equation). The LCD here is 3x:
\n" ); document.write( " $\"3x%284%2Fx+%2B+7%29+=+3x%282%2F%283x%29%29\"$
\n" ); document.write( "On the left side we need to use the Distributive Property:
\n" ); document.write( " $\"3x%284%2Fx%29+%2B+3x%287%29+=+3x%282%2F%283x%29%29\"$
\n" ); document.write( "Now we can cancel:
\n" ); document.write( " $\"3cross%28x%29%284%2Fcross%28x%29%29+%2B+3x%287%29+=+cross%283x%29%282%2Fcross%283x%29%29\"$
\n" ); document.write( "leaving
\n" ); document.write( " $\"3%2A4+%2B+3x%287%29+=+2\"$
\n" ); document.write( "This is easy to solve:
\n" ); document.write( " $\"12+%2B+21x+=+2\"$
\n" ); document.write( " $\"21x+=+-10\"$
\n" ); document.write( " $\"x+=+%28-10%29%2F21\"$ \n" ); document.write( "

\n" );