Question

Review the equation used in writing a partial fraction decomposition.

Answer 1

Applying partial fractions, the system of equations that can be used to find the values of A and B is given as follows:

• 5A = -15.

• -2A + B = 10.

What is the partial fraction?

The partial fraction is given as follows:

$\frac{-15x + 10}{(5x - 2)^2} = \frac{A}{5x - 2} + \frac{B}{(5x - 2)^2}$

Applying the least common multiple at the right side, we have that:

$\frac{-15x + 10}{(5x - 2)^2} = \frac{A(5x - 2) + B}{(5x - 2)^2}$

$\frac{-15x + 10}{(5x - 2)^2} = \frac{5Ax - 2A + B}{(5x - 2)^2}$

Hence, comparing both sides of the equality:

• 5A = -15.

• -2A + B = 10.

More can be learned about partial fractions at brainly.com/question/24594390

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