document.write( "Question 114482: Good evening ma'am or sir I don't know how to get the values of x here in this equation (clue: there are 3 answers, 1 fraction and 2 whole numbers), will you please help me. This is the equation: x^2+2x+1/x^2+3x+2=x^2+5x+6/x^2+4x+3.
\n" ); document.write( "Thank you very much ma'am or sir. \n" ); document.write( "

Algebra.Com's Answer #83309 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
how to get the values of x here in this equation (clue: there are 3 answers, 1 fraction and 2 whole numbers), will you please help me. This is the equation: \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B2x%2B1%29%2F%28x%5E2%2B3x%2B2%29+=+%28x%5E2%2B5x%2B6%29%2F+%28x%5E2%2B4x%2B3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "We will try to factor what ever is possible to factor in order to simplify this equation: \r
\n" ); document.write( "\n" ); document.write( "first this quadratic trinomial where we recognize the square of sum \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2x%2B1+=++%28x%2B1%29%5E2+=+%28x%2B1%29%28x%2B1%29\"$ ЕЕЕЕЕЕЕЕ.(1)\r
\n" ); document.write( "\n" ); document.write( "Now factor this one
\n" ); document.write( " $\"x%5E2%2B3x%2B2\"$ ЕЕ.we can replace $\"3x\"$ with $\"1x+%2B+2x\"$
\n" ); document.write( "
\n" ); document.write( " $\"x%5E2%2B1x+%2B+2x+%2B2\"$ ЕЕ.group first two terms and last two terms together
\n" ); document.write( "
\n" ); document.write( " $\"%28x%5E2%2B1x%29+%2B+%282x+%2B2%29\"$ ЕЕ.notice that $\"x\"$ is common for first group and $\"2\"$ is common for second group; so factor them out\r
\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B1%29+%2B+2%28x+%2B1%29\"$ ЕЕ. Factor out common $\"x%2B1\"$ , combine like terms\r
\n" ); document.write( "\n" ); document.write( " $\"+%28x%2B1%29+%28x+%2B+2%29+\"$ ЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕ.(2)\r
\n" ); document.write( "\n" ); document.write( "Now factor this one\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2+%2B+5x+%2B+6\"$ ЕЕЕ.. replace $\"5x+\"$ with $\"2x%2B3x\"$
\n" ); document.write( "
\n" ); document.write( " $\"x%5E2+%2B+2x+%2B+3x+%2B+6\"$ ЕЕЕ.. group first two terms and last two terms together\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2+%2B+2x+%29%2B%28+3x+%2B+6%29\"$ ЕЕЕ.. factor a $\"1x\"$ out of the first group and factor a $\"3\"$ out of the second group\r
\n" ); document.write( "\n" ); document.write( " $\"x%28x+%2B+2+%29+%2B+3%28x+%2B+2%29\"$ ЕЕЕ.. combine like terms
\n" ); document.write( "
\n" ); document.write( " $\"+%28x+%2B+2+%29+%28x+%2B+3%29+\"$ ЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕ..(3)\r
\n" ); document.write( "\n" ); document.write( "Now factor this one
\n" ); document.write( "
\n" ); document.write( " $\"x%5E2%2B4x%2B3\"$ ЕЕЕЕЕЕ. replace $\"4x+\"$ with $\"1x%2B3x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B1x%2B3x+%2B3\"$ ЕЕ. group first two terms and last two terms together\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B1x%29+%2B+%283x+%2B3%29\"$ ЕЕ. factor a $\"1x\"$ out of the first group and factor a $\"3\"$ out of the second group\r
\n" ); document.write( "\n" ); document.write( " $\"x%28x%2B1%29+%2B+3%28x+%2B+1%29\"$ ЕЕ. combine like terms
\n" ); document.write( " $\"+%28x%2B1%29+%28x+%2B+3%29+\"$ ЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕЕ.(4)\r
\n" ); document.write( "\n" ); document.write( "Now substitute (1), (2), (3), and (4) in original equation:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2B2x%2B1%29%2F%28x%5E2%2B3x%2B2%29+=+%28x%5E2%2B5x%2B6%29%2F+%28x%5E2%2B4x%2B3%29\"$ \r
\n" ); document.write( "\n" ); document.write( "

Е.. simplify\r
\n" ); document.write( "\n" ); document.write( " $\"+%28x%2B1%29%2F+%28x+%2B+2%29+=++%28x+%2B+2+%29++%2F+%28x%2B1%29++\"$ Е.....here we have denominators $\"x%2B2\"$ and $\"x%2B1\"$ ; they cannot be equal to $\"0\"$ ( to divide by $\"0\"$ doesn't make sense\r
\n" ); document.write( "\n" ); document.write( "so we will find values of $\"x\"$ for which it will be equal to $\"0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "they would be equal to $\"0\"$ if:\r
\n" ); document.write( "\n" ); document.write( " $\"x%2B2+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"x+=+-2\"$ .........................one $\"solution\"$ }\r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( " $\"x%2B1=0\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"x=-1\"$ ........................second $\"solution\"$ }\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find third solution:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+%28x%2B1%29%28x%2B1%29+=++%28x+%2B+2+%29%28x+%2B+2%29+\"$ Е..multiply\r
\n" ); document.write( "\n" ); document.write( " $\"+x%5E2%2B+2x+%2B+1+=++x%5E2+%2B+4x+%2B+4+\"$ Е.....simplify (eliminate $\"x%5E2\"$ on both sides\r
\n" ); document.write( "\n" ); document.write( " $\"+2x+%2B+1+=+4x+%2B+4+\"$ Е.....move $\"2x\"$ to the right and $\"4\"$ to the left\r
\n" ); document.write( "\n" ); document.write( " $\"1+-+4+=+4x+-2x+\"$ Е.....\r
\n" ); document.write( "\n" ); document.write( " $\"-+3+=+2x+\"$ Е.....divide both sides by $\"2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-+3%2F2+=+2x%2F2+\"$ Е.....\r
\n" ); document.write( "\n" ); document.write( " $\"-+3%2F2+=+x+\"$ Е.....\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+-3%2F2\"$ Е.......................third $\"solution\"$ }\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );