document.write( "Question 174167: 5/3x-1 - x-7/9x^-1=-2/3x+1
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Algebra.Com's Answer #129354 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

You can put this solution on YOUR website!
Assume that the problem is actually:
\n" ); document.write( " $\"5%2F%28%283x-1%29%29\"$ - $\"%28%28x-7%29%29%2F%28%289x%5E2-1%29%29\"$ = $\"-2%2F%28%283x%2B1%29%29\"$
\n" ); document.write( ":
\n" ); document.write( "(9x^2-1) is difference of squares, factor this:
\n" ); document.write( " $\"5%2F%28%283x-1%29%29\"$ - $\"%28%28x-7%29%29%2F%28%283x%2B1%29%283x%2B1%29%29\"$ = $\"-2%2F%28%283x%2B1%29%29\"$
\n" ); document.write( ":
\n" ); document.write( "Multiply equation by (3x+1)(3x-1)
\n" ); document.write( "(3x+1)(3x-1)* $\"5%2F%28%283x-1%29%29\"$ - (3x+1)(3x-1)* $\"%28%28x-7%29%29%2F%28%283x%2B1%29%283x%2B1%29%29\"$ = (3x+1)(3x-1)* $\"-2%2F%28%283x%2B1%29%29\"$
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\n" ); document.write( "Cancel out the denominators:
\n" ); document.write( "5(3x+1) - (x-7) = -2(3x-1)
\n" ); document.write( ":
\n" ); document.write( "15x + 5 - x + 7 = -6x + 2
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\n" ); document.write( "14x + 12 = -6x + 2
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\n" ); document.write( "14x + 6x = 2 - 12
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\n" ); document.write( "20x = -10
\n" ); document.write( "x = $\"%28-10%29%2F20\"$
\n" ); document.write( "x = $\"-1%2F2\"$
\n" ); document.write( ":
\n" ); document.write( "You can check the solution in the original equation using x=-.5
\n" ); document.write( " $\"5%2F%28%283%28-.5%29-1%29%29\"$ - $\"%28%28-.5-7%29%29%2F%28%289%28-.5%5E2%29-1%29%29\"$ = $\"-2%2F%28%283%28-.5%29%2B1%29%29\"$ \n" ); document.write( "

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