Divide ((s^2-2s)/(s^2+3s-10))/((s-5)/(s+5))

$\frac{\frac{s^{2} - 2 s}{s^{2} + 3 s - 10}}{\frac{s - 5}{s + 5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{s^{2} - 2 s}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Step 2

Factor $s$ out of $s^{2} - 2 s$ .

Factor $s$ out of $s^{2}$ .

$\frac{s \cdot s - 2 s}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Factor $s$ out of $- 2 s$ .

$\frac{s \cdot s + s \cdot - 2}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Factor $s$ out of $s \cdot s + s \cdot - 2$ .

$\frac{s (s - 2)}{s^{2} + 3 s - 10} \cdot \frac{s + 5}{s - 5}$

Step 3

Factor $s^{2} + 3 s - 10$ 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 $- 10$ and whose sum is $3$ .

$- 2, 5$

Write the factored form using these integers.

$\frac{s (s - 2)}{(s - 2) (s + 5)} \cdot \frac{s + 5}{s - 5}$

Step 4

Cancel the common factor of $s + 5$ .

Factor $s + 5$ out of $(s - 2) (s + 5)$ .

$\frac{s (s - 2)}{(s + 5) (s - 2)} \cdot \frac{s + 5}{s - 5}$

Cancel the common factor.

$\frac{s (s - 2)}{(s + 5) (s - 2)} \cdot \frac{s + 5}{s - 5}$

Rewrite the expression.

$\frac{s (s - 2)}{s - 2} \cdot \frac{1}{s - 5}$

Step 5

Multiply $\frac{s (s - 2)}{s - 2}$ by $\frac{1}{s - 5}$ .

$\frac{s (s - 2)}{(s - 2) (s - 5)}$

Step 6

Cancel the common factor of $s - 2$ .

Cancel the common factor.

$\frac{s (s - 2)}{(s - 2) (s - 5)}$

Rewrite the expression.

$\frac{s}{s - 5}$

Divide ((s^2-2s)/(s^2+3s-10))/((s-5)/(s+5))

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