Final answer:
The partial fraction decomposition of the given fraction is expressed as a sum of simpler fractions with unknown constants A and B. By multiplying both sides of the equation by the common denominator and equating coefficients, we can determine the values of A and B.
Step-by-step explanation:
To find the partial fraction decomposition of StartFraction 35 minus 27 x Over 4 x squared plus 28 x EndFraction, we need to factor the denominator and express the given fraction as a sum of simpler fractions. In this case, the denominator can be factored as 4x(x + 7).
The partial fraction decomposition is:
StartFraction 35 minus 27 x Over 4 x squared plus 28 x EndFraction = StartFraction A Over 4x EndFraction + StartFraction B Over x + 7 EndFraction
To determine the values of A and B, we can multiply both sides of the equation by the common denominator (4x(x + 7)) and then compare the coefficient of each term. By equating the coefficients, we can solve for A and B.