Basic Math Examples

$\frac{49 r^{2} s^{3}}{7 r - 14} \cdot \frac{98 - 49 r}{14 r^{3} s}$

Step 1

Factor $7$ out of $7 r - 14$ .

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Step 1.1

Factor $7$ out of $7 r$ .

$\frac{49 r^{2} s^{3}}{7 (r) - 14} \cdot \frac{98 - 49 r}{14 r^{3} s}$

Step 1.2

Factor $7$ out of $- 14$ .

$\frac{49 r^{2} s^{3}}{7 r + 7 \cdot - 2} \cdot \frac{98 - 49 r}{14 r^{3} s}$

Step 1.3

Factor $7$ out of $7 r + 7 \cdot - 2$ .

$\frac{49 r^{2} s^{3}}{7 (r - 2)} \cdot \frac{98 - 49 r}{14 r^{3} s}$

Step 2

Factor $49$ out of $98 - 49 r$ .

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Step 2.1

Factor $49$ out of $98$ .

$\frac{49 r^{2} s^{3}}{7 (r - 2)} \cdot \frac{49 (2) - 49 r}{14 r^{3} s}$

Step 2.2

Factor $49$ out of $- 49 r$ .

$\frac{49 r^{2} s^{3}}{7 (r - 2)} \cdot \frac{49 (2) + 49 (- r)}{14 r^{3} s}$

Step 2.3

Factor $49$ out of $49 (2) + 49 (- r)$ .

$\frac{49 r^{2} s^{3}}{7 (r - 2)} \cdot \frac{49 (2 - r)}{14 r^{3} s}$

Step 3

Combine.

$\frac{49 r^{2} s^{3} (49 (2 - r))}{7 (r - 2) (14 r^{3} s)}$

Step 4

Cancel the common factor of $49$ and $7$ .

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Step 4.1

Factor $7$ out of $49 r^{2} s^{3} (49 (2 - r))$ .

$\frac{7 (7 r^{2} s^{3} (49 (2 - r)))}{7 (r - 2) (14 r^{3} s)}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $7$ out of $7 (r - 2) (14 r^{3} s)$ .

$\frac{7 (7 r^{2} s^{3} (49 (2 - r)))}{7 ((r - 2) (14 r^{3} s))}$

Step 4.2.2

Cancel the common factor.

$\frac{7 (7 r^{2} s^{3} (49 (2 - r)))}{7 ((r - 2) (14 r^{3} s))}$

Step 4.2.3

Rewrite the expression.

$\frac{7 r^{2} s^{3} (49 (2 - r))}{(r - 2) (14 r^{3} s)}$

Step 5

Cancel the common factor of $7$ and $14$ .

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Step 5.1

Factor $7$ out of $7 r^{2} s^{3} (49 (2 - r))$ .

$\frac{7 (r^{2} s^{3} (49 (2 - r)))}{(r - 2) (14 r^{3} s)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $7$ out of $(r - 2) (14 r^{3} s)$ .

$\frac{7 (r^{2} s^{3} (49 (2 - r)))}{7 ((r - 2) (2 r^{3} s))}$

Step 5.2.2

Cancel the common factor.

$\frac{7 (r^{2} s^{3} (49 (2 - r)))}{7 ((r - 2) (2 r^{3} s))}$

Step 5.2.3

Rewrite the expression.

$\frac{r^{2} s^{3} (49 (2 - r))}{(r - 2) (2 r^{3} s)}$

Step 6

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

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Step 6.1

Factor $r^{2}$ out of $r^{2} s^{3} (49 (2 - r))$ .

$\frac{r^{2} (s^{3} (49 (2 - r)))}{(r - 2) (2 r^{3} s)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $r^{2}$ out of $(r - 2) (2 r^{3} s)$ .

$\frac{r^{2} (s^{3} (49 (2 - r)))}{r^{2} ((r - 2) (2 r s))}$

Step 6.2.2

Cancel the common factor.

$\frac{r^{2} (s^{3} (49 (2 - r)))}{r^{2} ((r - 2) (2 r s))}$

Step 6.2.3

Rewrite the expression.

$\frac{s^{3} (49 (2 - r))}{(r - 2) (2 r s)}$

Step 7

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

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Step 7.1

Factor $s$ out of $s^{3} (49 (2 - r))$ .

$\frac{s (s^{2} (49 (2 - r)))}{(r - 2) (2 r s)}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $s$ out of $(r - 2) (2 r s)$ .

$\frac{s (s^{2} (49 (2 - r)))}{s ((r - 2) (2 r))}$

Step 7.2.2

Cancel the common factor.

$\frac{s (s^{2} (49 (2 - r)))}{s ((r - 2) (2 r))}$

Step 7.2.3

Rewrite the expression.

$\frac{s^{2} (49 (2 - r))}{(r - 2) (2 r)}$

Step 8

Cancel the common factor of $2 - r$ and $r - 2$ .

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Step 8.1

Rewrite $2$ as $- 1 (- 2)$ .

$\frac{s^{2} (49 (- 1 (- 2) - r))}{(r - 2) (2 r)}$

Step 8.2

Factor $- 1$ out of $- r$ .

$\frac{s^{2} (49 (- 1 (- 2) - (r)))}{(r - 2) (2 r)}$

Step 8.3

Factor $- 1$ out of $- 1 (- 2) - (r)$ .

$\frac{s^{2} (49 (- 1 (- 2 + r)))}{(r - 2) (2 r)}$

Step 8.4

Reorder terms.

$\frac{s^{2} \cdot 49 (- 1 (r - 2))}{(r - 2) \cdot 2 r}$

Step 8.5

Cancel the common factor.

$\frac{s^{2} \cdot 49 (- 1 (r - 2))}{(r - 2) \cdot 2 r}$

Step 8.6

Rewrite the expression.

$\frac{s^{2} \cdot 49 \cdot (- 1)}{2 r}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $- 1$ by $49$ .

$\frac{s^{2} \cdot - 49}{2 r}$

Step 9.2

Move $- 49$ to the left of $s^{2}$ .

$\frac{- 49 \cdot s^{2}}{2 r}$

Step 9.3

Move the negative in front of the fraction.

$- \frac{49 s^{2}}{2 r}$