SOLUTION: What is d^2+3d/ d^2-2d minus -4/d?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What is d^2+3d/ d^2-2d minus -4/d?      Log On


   

Question 243034: What is d^2+3d/ d^2-2d minus -4/d?
Found 2 solutions by checkley77, oberobic:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(d^2+3d)/(d^2-2d)-(-4/d)
d(d+3)/d(d-2)+4/d cancel out the d fron the first fraction
(d+3)/(d-2)+4/d find LCD & add.
[d(d+3)+4(d-2)]/d(d-2)
(d^2+3d+4d-8)/d(d-2)
(d^2+7d-8)/d(d-2)
(d+8)(d-1)/d(d-2) ans.

Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
+%0D%0A%28%28d%5E2%2B3d%29%2F%28d%5E2-2d%29%29-%28-4%2Fd%29%0D%0A
...
Minus a -4/d is the same as adding it.
+%0D%0A%28%28d%5E2%2B3d%29%2F%28d%5E2-2d%29%29%2B%284%2Fd%29%0D%0A
...
You can factor a 'd' from the numerator and denominator of the first part:
+%0D%0A%28d%28d%2B3%29%2Fd%28d-2%29%29%2B%284%2Fd%29%0D%0A
...
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:
+%0D%0A%28%28d%2B3%29%2F%28d-2%29%29%2B%284%2Fd%29%0D%0A
...
Solving any faction, we create a common denominator, which in this case would be:
%0D%0Ad%2A%28d-2%29%0D%0A
...
%0D%0Ad%28d%2B3%29%2Fd%28d-2%29+%2B+4%28d-2%29%2Fd%28d-2%29%0D%0A
...
Now we simply combine the fractions:
%0D%0A%28d%28d%2B3%29+%2B+4%28d-2%29%29+%2F+d%28d-2%29%0D%0A
...
%0D%0A%28d%5E2+%2B+3d+%2B+4d+-+8%29+%2F+d%28d-2%29%0D%0A
...
%0D%0A%28d%5E2+%2B+7d+-+8%29+%2F+d%28d-2%29%0D%0A
...
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.
%0D%0A%28%28d+-+1%29%28d+%2B+8%29%29+%2F+d%28d-2%29%0D%0A
...
That's as far as we can go.