What is (x+13}{x^3(3-x)}*\frac{x(x-3))/5 ?

The solution to (x+13}{x^3(3-x)}*\frac{x(x-3))/5 is -(x+13)/(5x^2)

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simplify (x+13}{x^3(3-x)}*\frac{x(x-3))/5

simplify

\frac{x + 13}{x ^{3} ( 3 - x )} \cdot \frac{x ( x - 3 )}{5}

- \frac{x + 13}{5 x ^{2}}

Solution steps

\frac{x + 13}{x ^{3} ( 3 - x )} \cdot \frac{x ( x - 3 )}{5}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( x + 13 ) x ( x - 3 )}{x ^{3} ( 3 - x ) \cdot 5}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{3} = x x^{2}

= \frac{( x + 13 ) x ( x - 3 )}{x x ^{2} ( 3 - x ) \cdot 5}

Cancel the common factor:

x

= \frac{( x + 13 ) ( x - 3 )}{x ^{2} ( 3 - x ) \cdot 5}

x^{2} (3 - x) \cdot 5 = - x^{2} (x - 3) \cdot 5

= \frac{( x + 13 ) ( x - 3 )}{- x ^{2} ( x - 3 ) \cdot 5}

Cancel the common factor:

x - 3

= \frac{x + 13}{- x ^{2} \cdot 5}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{x + 13}{x ^{2} \cdot 5}

= - \frac{x + 13}{5 x ^{2}}

\frac{4}{x} + \frac{5}{6}

x^{2} + 2 + \frac{1}{x ^{2}}

\frac{3}{45}

\frac{5 ^{13} \cdot 5 ^{17}}{5 ^{11} \cdot 5 ^{16} \cdot 5}

\frac{12}{( - 4 )}

What is (x+13}{x^3(3-x)}*\frac{x(x-3))/5 ?
The solution to (x+13}{x^3(3-x)}*\frac{x(x-3))/5 is -(x+13)/(5x^2)