Question 76095
{{{5/(y-3) - 30 /(y^2-9) = 1}}}
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The denominator {{{y^2-9}}} is the difference of two squares. The rule that applies to
factoring the difference between two squares is:
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{{{a^2 - b^2 = (a + b)*(a - b)}}}
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Applying this rule to {{{y^2 - 9}}} results in:
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{{{y^2 - 9= (y + 3)*(y - 3)}}}
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Substituting this into the equation changes the equation to:
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{{{5/(y-3) - 30/((y+3)*(y-3)) = 1}}}
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You can get all the terms over the common denominator of {{{(y + 3)*(y - 3)}}}.  Multiply the
first term by {{{(y+3)/(y+3)}}} which is the same as multiplying the first term by 1 because
the numerator of this multiplier is the same as the denominator.  When you do this 
multiplication the equation becomes:
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{{{5(y+3)/((y+3)*(y-3)) - 30/((y+3)*(y-3)) = 1}}}
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Then multiply the 1 on the right side by {{{((y+3)*(y-3))/((y+3)*(y-3))}}}. This multiplication
results in:
{{{5(y+3)/((y+3)*(y-3)) - 30/((y+3)*(y-3)) = ((y+3)*(y-3))/((y+3)*(y-3))}}}
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Now you can multiply the entire equation (both sides, all terms) by the common denominator
{{{ ((y+3)*(y-3))}}} and after that multiplication you are left with only the numerators
of all the terms in the equation.  The result is:
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{{{5*(y+3) - 30 = (y + 3)*(y - 3)}}}
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Multiply where called for and the equation becomes:
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{{{5y + 15 - 30 = y^2 - 9}}}
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Subtract {{{y^2-9}}} from both sides to get:
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{{{5y + 15 - 30 - y^2 + 9 = 0}}}
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Rearrange terms in descending powers of y:
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{{{-y^2 + 5y + 15 - 30 + 9 = 0}}}
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Combine the constants:
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{{{-y^2 + 5y - 6 = 0}}}
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Multiply the entire equation (both sides and all terms) by -1 to get:
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{{{y^2 - 5y + 6 = 0}}}
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This factors to:
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{{{(y-3)*(y-2) = 0}}}
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If either of the factors equals zero, then the equation is true because a multiplication
by zero on the left side, makes the entire left side equal to the zero on the right side.
Find the solutions for y by setting each of the factors equal to zero and solving for
y ...
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y - 2 = 0 <---- add 2 to both sides
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y = +2  <--- one answer for y
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y - 3 = 0 <--- add 3 to both sides
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y = +3 <--- the second answer for y
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But the second answer [y = +3] is not permitted because this would cause a division by
zero in the second term of the original equation ... the denominator of the second term
is {{{y^2 - 9}}} and it is equal to {{{(y+3)*(y-3)}}} and if y is allowed to equal
+3 then one of the factors in the denominator is zero ... and division by zero is not 
permitted.
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So there you are ... the answer to the equation is y = +2.
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Hope this helps you to understand the problem a little better.