What is A/((x-0.5)^3)+B/((x-0.5)^2) ?

The solution to A/((x-0.5)^3)+B/((x-0.5)^2) is (A+Bx-0.5B)/((x-0.5)^3)

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simplify A/((x-0.5)^3)+B/((x-0.5)^2)

simplify

\frac{A}{( x - 0.5 ) ^{3}} + \frac{B}{( x - 0.5 ) ^{2}}

\frac{A + B x - 0.5 B}{( x - 0.5 ) ^{3}}

Solution steps

\frac{A}{( x - 0.5 ) ^{3}} + \frac{B}{( x - 0.5 ) ^{2}}

Least Common Multiplier of

(x - 0.5)^{3}, (x - 0.5)^{2} : (x - 0.5)^{3}

Adjust Fractions based on the LCM

= \frac{A}{( x - 0.5 ) ^{3}} + \frac{B ( x - 0.5 )}{( x - 0.5 ) ^{3}}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{A + B ( x - 0.5 )}{( x - 0.5 ) ^{3}}

Simplify

A + B (x - 0.5) : A + B x - 0.5 B

= \frac{A + B x - 0.5 B}{( x - 0.5 ) ^{3}}

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What is A/((x-0.5)^3)+B/((x-0.5)^2) ?
The solution to A/((x-0.5)^3)+B/((x-0.5)^2) is (A+Bx-0.5B)/((x-0.5)^3)