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

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

Step 1

Simplify the denominator.

Rewrite $25$ as $5^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 5$ .

$\frac{3 x^{3}}{(x + 5) (x - 5)} \cdot \frac{x^{2} + 6 x + 5}{x^{2}}$

Step 2

Factor $x^{2} + 6 x + 5$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $5$ and whose sum is $6$ .

$1, 5$

Write the factored form using these integers.

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

Step 3

Simplify terms.

Combine.

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

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $3 x^{3} ((x + 1) (x + 5))$ .

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

Cancel the common factors.

Factor $x^{2}$ out of $(x + 5) (x - 5) x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 x ((x + 1) (x + 5))}{(x + 5) (x - 5)}$

Cancel the common factor of $x + 5$ .

Cancel the common factor.

$\frac{3 x ((x + 1) (x + 5))}{(x + 5) (x - 5)}$

Rewrite the expression.

$\frac{3 x (x + 1)}{x - 5}$

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

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