document.write( "Question 99549: Tutor, \r
\n" ); document.write( "\n" ); document.write( "I was wondering if I solved these problems correctly would you be able to help me? \r
\n" ); document.write( "\n" ); document.write( "1.) Solve: x/(5x+10) + (x-3)/(x+2) = 7/5 is the answer -17 ?
\n" ); document.write( "2.) write in simplest form: x^2 - 12x + 27 / x^2 - 81 is the answer x+3/x-9? \r
\n" ); document.write( "\n" ); document.write( "I am not sure I solved these correctly so any help is appreciated. Thank you. \n" ); document.write( "
Algebra.Com's Answer #72407 by bucky(2189)\"\" \"About 
You can put this solution on YOUR website!
Both problems need a little work.
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\n" ); document.write( "First problem:
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\n" ); document.write( "Given:
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\n" ); document.write( "\"x%2F%285x%2B10%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5\"
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\n" ); document.write( "If you factor the denominator of the first term you get:
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\n" ); document.write( "\"x%2F%285%28x%2B2%29%29+%2B+%28x-3%29%2F%28x%2B2%29+=+7%2F5\"
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\n" ); document.write( "Next, give the second term the same denominator as the first term by multiplying it by 5.
\n" ); document.write( "You must also multiply the numerator of this second term by 5. The result is that the
\n" ); document.write( "equation then becomes:
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\n" ); document.write( "\"x%2F%285%28x%2B2%29%29+%2B+%285%2A%28x-3%29%29%2F%285%2A%28x%2B2%29%29+=+7%2F5\"
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\n" ); document.write( "Now, both terms on the left side have the same denominator, so you can add their numerators
\n" ); document.write( "and place that sum over the common denominator to get:
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\n" ); document.write( "\"%28x+%2B+5%2A%28x-3%29%29%2F%285%2A%28x%2B2%29%29+=+7%2F5\"
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\n" ); document.write( "Do the distributed multiplication in the numerator by multiplying 5 times each of the two
\n" ); document.write( "terms in the parentheses to get:
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\n" ); document.write( "\"%28x+%2B+5x+-+15%29%2F%285%2A%28x%2B2%29%29+=+7%2F5\"
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\n" ); document.write( "In the numerator, combine the terms containing x to get:
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\n" ); document.write( "\"%286x+-+15%29%2F%285%2A%28x%2B2%29%29+=+7%2F5\"
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\n" ); document.write( "Get rid of the denominator on the left side by multiplying both sides of this equation by
\n" ); document.write( "\"5%2A%28x%2B2%29\". When you do that the equation becomes:
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\n" ); document.write( "\"6x+-+15+=+%287%2F5%29%2A%285%29%2A%28x%2B2%29\"
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\n" ); document.write( "Notice on the right side that the multiplier of 5 is in the numerator and it will cancel
\n" ); document.write( "with the 5 in the denominator of the \"7%2F5\". As a result the equation reduces to:
\n" ); document.write( ".
\n" ); document.write( "\"6x+-+15+=+7%2A%28x%2B2%29\"
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\n" ); document.write( "Do the distributed multiplication on the right side by multiplying 7 times each of the
\n" ); document.write( "terms in the parentheses to get:
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\n" ); document.write( "\"6x+-+15+=+7x+%2B+14\"
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\n" ); document.write( "Get rid of the 7x on the right side by subtracting 7x from both sides. This changes the
\n" ); document.write( "equation to:
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\n" ); document.write( "\"-x+-+15+=+14\"
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\n" ); document.write( "Get rid of the -15 on the left side by adding +15 to both sides. This converts the equation
\n" ); document.write( "to:
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\n" ); document.write( "\"-x+=+29\"
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\n" ); document.write( "Finally, solve for +x by either dividing both sides by -1 or multiplying both sides by
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\n" ); document.write( "In the second problem, I suspect that you might have made a mistake in factoring the numerator
\n" ); document.write( "because you were very close to the right answer. You were given:
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\n" ); document.write( "\"%28x%5E2+-+12x+%2B+27%29+%2F+%28x%5E2+-+81%29\"
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\n" ); document.write( "Both the numerator and the denominator will factor, and you can then cancel the factors that
\n" ); document.write( "are common to the numerator and the denominator. When you do the factoring you get:
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\n" ); document.write( "\"%28%28x-9%29%2A%28x-3%29%29%2F%28%28x%2B9%29%2A%28x-9%29%29\"
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\n" ); document.write( "[You can multiply (x-9) times (x-3) to convince yourself that the product of these two
\n" ); document.write( "factors is \"x%5E2+-+12x+%2B+27\"]
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\n" ); document.write( "Now cancel the common factors:
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\n" ); document.write( "\"%28%28cross%28x-9%29%29%2A%28x-3%29%29%2F%28%28x%2B9%29%28cross%28x-9%29%29%29\"
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\n" ); document.write( "and you are left with the answer of:
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\n" ); document.write( "\"%28x-3%29%2F%28x%2B9%29\"
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\n" ); document.write( "This differs from your answer only by the minus sign in the numerator and the plus sign
\n" ); document.write( "in the denominator.
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\n" ); document.write( "Hope this helps you to identify your minor errors that you made in these two problems.
\n" ); document.write( "You seem to have the right idea of what to do but are just making minor mistakes which you
\n" ); document.write( "will be able to eliminate with a little more practice. Keep up the good work.
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