document.write( "Question 173560: 5/y-3=y+7/2y-6+1 I need help solving this \n" ); document.write( "
Algebra.Com's Answer #128704 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
5/y-3=y+7/2y-6+1
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document.write( "Hmmm! You didn't put parentheses to show where numerators \r\n" );
document.write( "and denominators begin \"(\" and end \")\", so I'm guessing you\r\n" );
document.write( "mean one of two possibilities.  I'll do both:\r\n" );
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document.write( "If you mean this:\r\n" );
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document.write( "\"matrix%281%2C5%2C+5%2F%28y-3%29%2C%22=%22%2C%28y%2B7%29%2F%282y-6%29%2C%22%2B%22%2C1%29\"\r\n" );
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document.write( "Write the \"1\" as \"1%2F1\" so every term will\r\n" );
document.write( "be a fraction:\r\n" );
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document.write( "\"matrix%281%2C5%2C+5%2F%28y-3%29%2C%22=%22%2C%28y%2B7%29%2F%282y-6%29%2C%22%2B%22%2C1%2F1%29\"\r\n" );
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document.write( "Enclose each term in parentheses:\r\n" );
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document.write( "Factor the denominator \"2y-6\" as \"2%28y-3%29\"\r\n" );
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document.write( "Find the LCD, which is \"2%28y-3%29\", which we will\r\n" );
document.write( "write as \"%28%282%28y-3%29%29%2F1%29\" and multiply each term\r\n" );
document.write( "by it:\r\n" );
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document.write( "Cancel what will cancel:\r\n" );
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document.write( "All that's left is:\r\n" );
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document.write( "\"matrix%281%2C3%2C2%2A5%2C%22=%22%2C+y%2B7%2B2%28y-3%29%29\"\r\n" );
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document.write( "Distribute:\r\n" );
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document.write( "\"matrix%281%2C3%2C2%2A5%2C%22=%22%2C+y%2B7%2B2y-6%29%29\"\r\n" );
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document.write( "Combine like terms:\r\n" );
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document.write( "\"matrix%281%2C3%2C10%2C%22=%22%2C+3y%2B1%29%29\"\r\n" );
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document.write( "Add -1 to both sides\r\n" );
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document.write( "\"matrix%281%2C3%2C9%2C%22=%22%2C3y%29\"\r\n" );
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document.write( "Divide both sides by 3:\r\n" );
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document.write( "\"matrix%281%2C3%2C3%2C%22=%22%2Cy%29\"\r\n" );
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document.write( "Now we must check this answer, by\r\n" );
document.write( "substituting it into the original, to make sure it\r\n" );
document.write( "is not an extraneous solution:\r\n" );
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document.write( "\"matrix%281%2C5%2C+5%2F%28y-3%29%2C%22=%22%2C%28y%2B7%29%2F%282y-6%29%2C%22%2B%22%2C1%29\"\r\n" );
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document.write( "\"matrix%281%2C5%2C+5%2F0%2C%22=%22%2C%28y%2B7%29%2F%286-6%29%2C%22%2B%22%2C1%29\"\r\n" );
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document.write( "\"matrix%281%2C5%2C+5%2F0%2C%22=%22%2C%28y%2B7%29%2F0%2C%22%2B%22%2C1%29\"\r\n" );
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document.write( "But since division by 0 is undefined, there is\r\n" );
document.write( "no solution. 3 was an extraneous, or \"bogus\"\r\n" );
document.write( "solution, not an actual solution.\r\n" );
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document.write( "If you meant this:\r\n" );
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document.write( "Use 1 denominators so that all terms will be\r\n" );
document.write( "fractions:\r\n" );
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document.write( "Enclose each term in parentheses:\r\n" );
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document.write( "Factor the denominator \"2y-6\" as \"2%28y-3%29\"\r\n" );
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document.write( "Find the LCD, which is \"2%28y-3%29\", which we will\r\n" );
document.write( "write as \"%28%282%28y-3%29%29%2F1%29\" and multiply each term\r\n" );
document.write( "by it:\r\n" );
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document.write( "Cancel what will cancel:\r\n" );
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document.write( "All that's left is:\r\n" );
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document.write( "\"matrix%281%2C7%2C+10%2C%22=%22%2C2y%28y-3%29%2C+%22%2B%22%2C+7%2C+%22%2B%22%2C+2%28y-3%29%29\"\r\n" );
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document.write( "Distribute to remove parentheses:\r\n" );
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document.write( "\"matrix%281%2C3%2C10%2C%22=%22%2C2y%5E2-6y%2B7%2B2y-6%29\"\r\n" );
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document.write( "Collect like terms:\r\n" );
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document.write( "\"matrix%281%2C3%2C10%2C%22=%22%2C2y%5E2-4y%2B1%29\"\r\n" );
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document.write( "Get 0 on the left by subtracting 10 from both sides:\r\n" );
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document.write( "\"matrix%281%2C3%2C0%2C%22=%22%2C2y%5E2-4y-9%29\"\r\n" );
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document.write( "or, since I like to have 0 on the right, not left,\r\n" );
document.write( "I'll switch the sides:\r\n" );
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document.write( "\"matrix%281%2C3%2C2y%5E2-4y-9%2C%22=%22%2C0%29\"\r\n" );
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document.write( "That doesn't factor, so we use the quadratic\r\n" );
document.write( "formula:\r\n" );
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document.write( "\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "\"y+=+%284+%2B-+sqrt%2816%2B72%29+%29%2F4+\"\r\n" );
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document.write( "\"y+=+%284+%2B-+sqrt%2888%29+%29%2F4+\"\r\n" );
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document.write( "\"y+=+%284+%2B-+sqrt%284%2A22%29+%29%2F4+\"\r\n" );
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document.write( "\"y+=+%284+%2B-+2sqrt%2822%29+%29%2F4+\"\r\n" );
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document.write( "Factor 2 out of the numerator:\r\n" );
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document.write( "\"y+=+%282%282+%2B-+sqrt%2822%29%29+%29%2F4+\"\r\n" );
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document.write( "Cancel the 2 on top into the 4 on the bottom,\r\n" );
document.write( "getting 2 on the bottom:\r\n" );
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document.write( "\"y+=+%28cross%282%29%282+%2B-+sqrt%2822%29%29+%29%2F%28cross%284%29%29%5B2%5D+\"\r\n" );
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document.write( "\"y+=+%282+%2B-+sqrt%2822%29+%29%2F2+\"\r\n" );
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document.write( "This is difficult to check. However if we were\r\n" );
document.write( "to substitute that in the original, none of the\r\n" );
document.write( "denominators would be 0, as they were in the\r\n" );
document.write( "first way I assumed you meant.  So these are both\r\n" );
document.write( "solutions.\r\n" );
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document.write( "Edwin
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