document.write( "Question 189707This question is from textbook Prentice Hall Algebra 1
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\n" ); document.write( "\n" ); document.write( "x-7/x+2 = 1/4\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance for anyone who can help!! :) I can't find a least common denominator.\r
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Algebra.Com's Answer #142347 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
Is the equation \"%28x-7%29%2F%28x%2B2%29+=+1%2F4+\" ???\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-7%29%2F%28x%2B2%29+=+1%2F4+\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"4%28x-7%29+=+1%28x%2B2%29\" Cross multiply\r
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\n" ); document.write( "\n" ); document.write( "\"4x-28=x%2B2\" Distribute.\r
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\n" ); document.write( "\n" ); document.write( "\"4x=x%2B2%2B28\" Add \"28\" to both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"4x-x=2%2B28\" Subtract \"x\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"3x=2%2B28\" Combine like terms on the left side.\r
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\n" ); document.write( "\n" ); document.write( "\"3x=30\" Combine like terms on the right side.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%2830%29%2F%283%29\" Divide both sides by \"3\" to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "\"x=10\" Reduce.\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the answer is \"x=10\" \r
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\n" ); document.write( "\n" ); document.write( "Is the equation \"x-7%2F%28x%2B2%29+=+1%2F4\" ????\r
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\n" ); document.write( "\n" ); document.write( "\"x-7%2F%28x%2B2%29+=+1%2F4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " Multiply EVERY term by the LCD \"4%28x%2B2%29\" to clear the fractions.\r
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\n" ); document.write( "\n" ); document.write( "\"4x%28x%2B2%29-4%287%29=x%2B2\" Simplify\r
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\n" ); document.write( "\n" ); document.write( "\"4x%28x%2B2%29-28=x%2B2\" Multiply\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2%2B8x-28=x%2B2\" Distribute\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2%2B8x-28-x-2=0\" Get everything to the left side\r
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\n" ); document.write( "\n" ); document.write( "\"4x%5E2%2B7x-30=0\" Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "Notice we have a quadratic equation in the form of \"ax%5E2%2Bbx%2Bc\" where \"a=4\", \"b=7\", and \"c=-30\"\r
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\n" ); document.write( "\n" ); document.write( "Let's use the quadratic formula to solve for x\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\" Start with the quadratic formula\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%287%29+%2B-+sqrt%28+%287%29%5E2-4%284%29%28-30%29+%29%29%2F%282%284%29%29\" Plug in \"a=4\", \"b=7\", and \"c=-30\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B-+sqrt%28+49-4%284%29%28-30%29+%29%29%2F%282%284%29%29\" Square \"7\" to get \"49\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B-+sqrt%28+49--480+%29%29%2F%282%284%29%29\" Multiply \"4%284%29%28-30%29\" to get \"-480\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B-+sqrt%28+49%2B480+%29%29%2F%282%284%29%29\" Rewrite \"sqrt%2849--480%29\" as \"sqrt%2849%2B480%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B-+sqrt%28+529+%29%29%2F%282%284%29%29\" Add \"49\" to \"480\" to get \"529\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B-+sqrt%28+529+%29%29%2F%288%29\" Multiply \"2\" and \"4\" to get \"8\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B-+23%29%2F%288%29\" Take the square root of \"529\" to get \"23\". \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%28-7+%2B+23%29%2F%288%29\" or \"x+=+%28-7+-+23%29%2F%288%29\" Break up the expression. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%2816%29%2F%288%29\" or \"x+=++%28-30%29%2F%288%29\" Combine like terms. \r
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\n" ); document.write( "\n" ); document.write( "\"x+=+2\" or \"x+=+-15%2F4\" Simplify. \r
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\n" ); document.write( "\n" ); document.write( "So the answers are \"x+=+2\" or \"x+=+-15%2F4\"\r
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\n" ); document.write( "\n" ); document.write( "Is the equation \"%28x-7%29%2Fx%2B2+=+1%2F4\" ????\r
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\n" ); document.write( "\n" ); document.write( "\"%28x-7%29%2Fx%2B2+=+1%2F4\" Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( "\"4%2Across%28x%29%28%28x-7%29%2Fcross%28x%29%29%2B8x+=+cross%284%29x%281%2Fcross%284%29%29\" Multiply EVERY term by the LCD \"4x\" to clear the fractions. \r
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\n" ); document.write( "\n" ); document.write( "\"4%28x-7%29%2B8x=x\" Simplify\r
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\n" ); document.write( "\n" ); document.write( "\"4x-28%2B8x=x\" Distribute.\r
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\n" ); document.write( "\n" ); document.write( "\"12x-28=x\" Combine like terms on the left side.\r
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\n" ); document.write( "\n" ); document.write( "\"12x=x%2B28\" Add \"28\" to both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"12x-x=28\" Subtract \"x\" from both sides.\r
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\n" ); document.write( "\n" ); document.write( "\"11x=28\" Combine like terms on the left side.\r
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\n" ); document.write( "\n" ); document.write( "\"x=%2828%29%2F%2811%29\" Divide both sides by \"11\" to isolate \"x\".\r
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\n" ); document.write( "\n" ); document.write( "Answer:\r
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\n" ); document.write( "\n" ); document.write( "So the answer is \"x=28%2F11\" which approximates to .
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