Solve (x-3)^5/2-(x-3)^(1/2)

Evaluate

\frac{( x - 3 ) ^{5}}{2} - (x - 3)^{\frac{1}{2}}

Reduce fractions to a common denominator

\frac{( x - 3 ) ^{5}}{2} - \frac{( x - 3 ) ^{\frac{1}{2}} \times 2}{2}

Write all numerators above the common denominator

\frac{( x - 3 ) ^{5} - ( x - 3 ) ^{\frac{1}{2}} \times 2}{2}

Expand the expression

\frac{x ^{5} - 15 x ^{4} + 90 x ^{3} - 270 x ^{2} + 405 x - 243 - ( x - 3 ) ^{\frac{1}{2}} \times 2}{2}

Use the commutative property to reorder the terms

\frac{x ^{5} - 15 x ^{4} + 90 x ^{3} - 270 x ^{2} + 405 x - 243 - 2 ( x - 3 ) ^{\frac{1}{2}}}{2}

Solution

\frac{x ^{5} - 15 x ^{4} + 90 x ^{3} - 270 x ^{2} + 405 x - 243 - 2 x - 3}{2}

Simplify the expression