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3 years ago

Simplify the following expression.( Fraction form) 7-5/6 * 7-7/6

Mathematics

1 answer:

Ipatiy [6.2K]3 years ago

5 0

Answer:

1295/36

Step-by-step explanation:

the statement tell us:

(7-(5/6))*(7-(7/6))

we have:

(7-(5/6))=((6*7)-5)/6=(42-5)/6=37/6

and we have:

(7-(7/6))=((6*7)-7)/6=(42-7)/6=35/6

we need multiply both terms:

(37/6)*(35/6)=(37*35)/(6*6)

finally we have

1295/36

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3 years ago

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Vladimir79 [104]

Answer:

-ln|x−5| + 2 ln(x²+4) + 3 tan⁻¹(x/2) + C

Step-by-step explanation:

The fraction will be split into a sum of two other fractions.

The first fraction will have a denominator of x − 5. The numerator will the a polynomial of one less order, in this case, a constant A.

The second fraction will have a denominator of x² + 4. The numerator will be Bx + C.

$\frac{3x^{2}-26x+26}{(x-5)(x^{2}+4)}=\frac{A}{x-5} +\frac{Bx+C}{x^{2}+4}$

Combine the two fractions back into one using the common denominator.

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This numerator will equal the original numerator.

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Match the coefficients.

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Solve the system of equations.

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$\int {(\frac{-1}{x-5}+\frac{4x-6}{x^{2}+4}) } \, dx$

Solving:

$\int {\frac{-1}{x-5}\, dx + \int {\frac{4x}{x^{2}+4}} \, dx - \int {\frac{6}{x^{2}+4} } \, dx$

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3 years ago

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Answer:

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