Question 243034
{{{ 
((d^2+3d)/(d^2-2d))-(-4/d)
}}}
...
Minus a -4/d is the same as adding it.
{{{ 
((d^2+3d)/(d^2-2d))+(4/d)
}}}
...
You can factor a 'd' from the numerator and denominator of the first part:
{{{ 
(d(d+3)/d(d-2))+(4/d)
}}}
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Then you can 'cancel' d/d because it is just 1.
You can factor a 'd' from the numerator and denominator of the first part:
{{{ 
((d+3)/(d-2))+(4/d)
}}}
...
Solving any faction, we create a common denominator, which in this case would be:
{{{
d*(d-2)
}}}
...
{{{
d(d+3)/d(d-2) + 4(d-2)/d(d-2)
}}}
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Now we simply combine the fractions:
{{{
(d(d+3) + 4(d-2)) / d(d-2)
}}}
...
{{{
(d^2 + 3d + 4d - 8) / d(d-2)
}}}
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{{{
(d^2 + 7d - 8) / d(d-2)
}}}
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Can we factor the quadratic in the numerator?  
Well, the factors of 8 are 1 * 8 and 2 * 4.  We know they are opposite sign  because we have -8.  And we need them to total 7, which we can do with +8 and -1.
{{{
((d - 1)(d + 8)) / d(d-2)
}}}
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That's as far as we can go.