What is (5x+25)/(x^3-x^2)*(x^2-1)/(x^2+6x+5) ?

The solution to (5x+25)/(x^3-x^2)*(x^2-1)/(x^2+6x+5) is 5/(x^2)

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simplify (5x+25)/(x^3-x^2)*(x^2-1)/(x^2+6x+5)

simplify

\frac{5 x + 25}{x ^{3} - x ^{2}} \cdot \frac{x ^{2} - 1}{x ^{2} + 6 x + 5}

\frac{5}{x ^{2}}

Solution steps

\frac{5 x + 25}{x ^{3} - x ^{2}} \cdot \frac{x ^{2} - 1}{x ^{2} + 6 x + 5}

Cancel

\frac{x ^{2} - 1}{x ^{2} + 6 x + 5} : \frac{x - 1}{x + 5}

= \frac{5 x + 25}{x ^{3} - x ^{2}} \cdot \frac{x - 1}{x + 5}

Apply the fraction rule:

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

= \frac{( 5 x + 25 ) ( x - 1 )}{( x ^{3} - x ^{2} ) ( x + 5 )}

Factor

5 x + 25 : 5 (x + 5)

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

Cancel the common factor:

x + 5

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

Factor

x^{3} - x^{2} : x^{2} (x - 1)

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

Cancel the common factor:

x - 1

= \frac{5}{x ^{2}}

(4 t^{5})^{3}

(x^{2} - x - 6) (x^{2} + 6 x + 9)

\frac{3}{7 x} - \frac{9}{x}

x - 9 x

I n (2)

What is (5x+25)/(x^3-x^2)*(x^2-1)/(x^2+6x+5) ?
The solution to (5x+25)/(x^3-x^2)*(x^2-1)/(x^2+6x+5) is 5/(x^2)