document.write( "Question 75319This question is from textbook Algebra 1 Concepts and Skills
\n" ); document.write( ": Hi I need help with rational equations. The directions say to solve the equation choosing a method.\r
\n" ); document.write( "\n" ); document.write( "42. x/9-8/x=1/9\r
\n" ); document.write( "\n" ); document.write( "43. (x+42)/x = x\r
\n" ); document.write( "\n" ); document.write( "If you can do these and explain them I would very much appreiciate it.\r
\n" ); document.write( "\n" ); document.write( "Thank You! \n" ); document.write( "
Algebra.Com's Answer #54141 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
42. x/9-8/x=1/9
\n" ); document.write( "\"x%2F9+-+8%2Fx\" = \"1%2F9\"
\n" ); document.write( ":
\n" ); document.write( "We want to get rid of the denominators, 9x is a common denominator so multiply
\n" ); document.write( "each term in the equation by 9x, this will cancel out the denominators and
\n" ); document.write( "give you:
\n" ); document.write( "x*x - 9(8) = x
\n" ); document.write( "x^2 - 72 = x
\n" ); document.write( ":
\n" ); document.write( "Subtract x from both sides and you have a quadratic equation:
\n" ); document.write( "x^2 - x - 72 = 0
\n" ); document.write( "Easily factored to:
\n" ); document.write( "(x-9)(x+8) = 0
\n" ); document.write( ":
\n" ); document.write( "x =+9 and x = -8
\n" ); document.write( ":
\n" ); document.write( "Substitute both of these in the original equation to check our solutions
\n" ); document.write( "x = 9
\n" ); document.write( "\"9%2F9+-+8%2F9\" = \"1%2F9\"
\n" ); document.write( "x = -8
\n" ); document.write( "\"-8%2F9+-+%288%2F-8%29\" = \"1%2F9%29\"
\n" ); document.write( "\"-8%2F9+%2B+%288%2F8%29\" = \"1%2F9%29\"
\n" ); document.write( "\"-8%2F9+%2B+1\" = \"1%2F9%29\"
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "43. (x+42)/x = x
\n" ); document.write( "\"%28%28x%2B42%29%29%2Fx\" = x
\n" ); document.write( ":
\n" ); document.write( "Multiply equation by x, gets rid of the denominator and you have;
\n" ); document.write( "x + 42 = x^2
\n" ); document.write( "0 = x^2 -x - 42; another easily factored quadratic equation:
\n" ); document.write( "(x-7)(x+6) = 0
\n" ); document.write( "x = +7 and x = -6
\n" ); document.write( ":
\n" ); document.write( "You can check the solutions by substituting both values in the original eq \n" ); document.write( "
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