Algebra Examples

$\frac{3 b - 5}{b^{2}} \cdot \frac{b^{4}}{5 - 3 b}$

Step 1

Cancel the common factor of $b^{2}$ .

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Step 1.1

Factor $b^{2}$ out of $b^{4}$ .

$\frac{3 b - 5}{b^{2}} \cdot \frac{b^{2} b^{2}}{5 - 3 b}$

Step 1.2

Cancel the common factor.

$\frac{3 b - 5}{b^{2}} \cdot \frac{b^{2} b^{2}}{5 - 3 b}$

Step 1.3

Rewrite the expression.

$(3 b - 5) \cdot \frac{b^{2}}{5 - 3 b}$

Step 2

Multiply $3 b - 5$ by $\frac{b^{2}}{5 - 3 b}$ .

$\frac{(3 b - 5) b^{2}}{5 - 3 b}$

Step 3

Cancel the common factor of $3 b - 5$ and $5 - 3 b$ .

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Step 3.1

Factor $- 1$ out of $3 b$ .

$\frac{(- (- 3 b) - 5) b^{2}}{5 - 3 b}$

Step 3.2

Rewrite $- 5$ as $- 1 (5)$ .

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

Step 3.3

Factor $- 1$ out of $- (- 3 b) - 1 (5)$ .

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

Step 3.4

Rewrite $- (- 3 b + 5)$ as $- 1 (- 3 b + 5)$ .

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

Step 3.5

Reorder terms.

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

Step 3.6

Cancel the common factor.

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

Step 3.7

Divide $- 1 b^{2}$ by $1$ .

$- 1 b^{2}$

Step 4

Rewrite $- 1 b^{2}$ as $- b^{2}$ .

$- b^{2}$