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Ksenya-84 [330]
3 years ago
11

6 and 3/5 - 4 and 3/4

Mathematics
2 answers:
Leni [432]3 years ago
4 0
1 and 17/20 should be the answer

Gwar [14]3 years ago
3 0
6 3/5 - 4 3/4?

This is pretty simple. First, you want to make the denominators the same, to make things easier. So find the LCM (Least Common Multiple), which is 20 in this case, and then multiply the 5 by 4 (to get 20) and vice versa for 4. Dont forget to multiply the numerator the same way. Now you should get something easier:

6 12/20 -4 15/20.

Now in this case, you must borrow a whole to finish this problem. So borrow a whole number from 6, (making it a 5) and bring it to the first fraction of the equation.

5 32/20 - 4 15/20.

Now, just solve. You should get  1 17/20. This cannot be simplified.
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9x-20/(x+6)^2 partial fraction decomposition
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We're looking for a,b such that

\dfrac{9x-20}{(x+6)^2}=\dfrac a{x+6}+\dfrac b{(x+6)^2}

Multiplying both sides by (x+6)^2 gives us

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Notice that when x=-6, the term involving a vanishes and we're left with

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Then

9x-20=a(x+6)-74=ax+6a-74\implies a=9

so that

\dfrac{9x-20}{(x+6)^2}=\boxed{\dfrac9{x+6}-\dfrac{74}{(x+6)^2}}

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