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tatuchka [14]
3 years ago
7

Blake burns 41/2 calories in 2/3 of a minute riding his bike. what is blakes unit rate

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
3 0
(9/2) (3)
--------- X -----
(2/3) (3)

(27/2)
---------
(2)

(27)
------
(4)

6 and (3/4) calories:1 minute
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What two rational expressions sum to 3x+4/x^2-6x+5?
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Answer:

\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}

Step-by-step explanation:

The given rational expression is:

\frac{3x+4}{x^{2}-6x+5} = \frac{3x+4}{(x-1)(x-5)}

We can use concept of Partial Fractions to solve this problem. Let,

\frac{3x+4}{(x-1)(x-5)}=\frac{A}{x-1} +\frac{B}{x-5}

Multiplying both sides by (x - 1)(x - 5), we get:

3x+4=A(x-5)+B(x-1)

Substituting x = 5, we get:

3(5)+4=A(5-5)+B(5-1)\\\\ 15+4=0+4B\\\\ 19=4B\\\\ B=\frac{19}{4}

Substituting x = 1, we get:

3(1)+4=A(1-5)+B(1-1)\\\\ 7=-4A\\\\ A=-\frac{7}{4}

Substituting the value of A and B, back in the original equation, we get:

\frac{3x+4}{x^2-6x+5}=\frac{-7}{4(x-1)} +\frac{19}{4(x-5)}

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