document.write( "Question 191816: 9*(x+2/x+3)^2-6*(x+2/x+3)+1=0 \n" ); document.write( "

Algebra.Com's Answer #143936 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Solve for x???
\n" ); document.write( " $\"9%2A%28%28x%2B2%29%2F%28x%2B3%29%29%5E2-6%2A%28%28x%2B2%29%2F%28x%2B3%29%29%2B1+=+0\"$
\n" ); document.write( "Just to facilitate solving, let's temporarily substitute: $\"z+=+%28%28x%2B2%29%2F%28x%2B3%29%29\"$ , so now we have:
\n" ); document.write( " $\"9z%5E2-6z%2B1+=+0\"$ Factor this quadratic equation.
\n" ); document.write( " $\"%283z-1%29%283z-1%29+=+0\"$ Apply the zero product rule:
\n" ); document.write( " $\"3z-1+=+0\"$ , so...
\n" ); document.write( " $\"3z+=+1\"$ and...
\n" ); document.write( " $\"z+=+1%2F3\"$ Now re-substitute $\"z+=+%28%28x%2B2%29%2F%28x%2B3%29%29\"$ to get:
\n" ); document.write( " $\"%28%28x%2B2%29%2F%28x%2B3%29%29+=+1%2F3\"$ Cross multiply.
\n" ); document.write( " $\"3%28x%2B2%29+=+%28x%2B3%29\"$ Simplify.
\n" ); document.write( " $\"3x%2B6+=+x%2B3\"$ Subtract x from both sides.
\n" ); document.write( " $\"2x%2B6+=+3\"$ Subtract 6 from both sides.
\n" ); document.write( " $\"2x+=+-3\"$ Finally, divide both sides by 2.
\n" ); document.write( " $\"highlight%28x+=+-3%2F2%29\"$
\n" ); document.write( "Check:
\n" ); document.write( " $\"9%2A%28%28x%2B2%29%2F%28x%2B3%29%29%5E2-6%2A%28%28x%2B3%29%2F%28x%2B2%29%29%2B1+=+0\"$ Substitute $\"x+=+-3%2F2\"$
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\n" ); document.write( " $\"9%2A%28%281%2F2%29%2F%283%2F2%29%29%5E2-6%2A%28%281%2F2%29%2F%283%2F2%29%29%2B1+=+0\"$ Simplify:
\n" ); document.write( " $\"9%2A%281%2F3%29%5E2-6%2A%281%2F3%29%2B1+=+0\"$
\n" ); document.write( " $\"9%2A%281%2F9%29-6%2A%281%2F3%29%2B1+=+0\"$
\n" ); document.write( " $\"1-2%2B1+=+0\"$
\n" ); document.write( " $\"0+=+0\"$ OK!
\n" ); document.write( " \n" ); document.write( "

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