Simplify (7b-14b^2)/(42b^2-21b)

$\frac{7 b - 14 b^{2}}{42 b^{2} - 21 b}$

Step 1

Factor $7 b$ out of $7 b - 14 b^{2}$ .

Factor $7 b$ out of $7 b$ .

$\frac{7 b (1) - 14 b^{2}}{42 b^{2} - 21 b}$

Factor $7 b$ out of $- 14 b^{2}$ .

$\frac{7 b (1) + 7 b (- 2 b)}{42 b^{2} - 21 b}$

Factor $7 b$ out of $7 b (1) + 7 b (- 2 b)$ .

$\frac{7 b (1 - 2 b)}{42 b^{2} - 21 b}$

$\frac{7 b (1 - 2 b)}{42 b^{2} - 21 b}$

Step 2

Factor $21 b$ out of $42 b^{2} - 21 b$ .

Factor $21 b$ out of $42 b^{2}$ .

$\frac{7 b (1 - 2 b)}{21 b (2 b) - 21 b}$

Factor $21 b$ out of $- 21 b$ .

$\frac{7 b (1 - 2 b)}{21 b (2 b) + 21 b (- 1)}$

Factor $21 b$ out of $21 b (2 b) + 21 b (- 1)$ .

$\frac{7 b (1 - 2 b)}{21 b (2 b - 1)}$

$\frac{7 b (1 - 2 b)}{21 b (2 b - 1)}$

Step 3

Cancel the common factor of $7$ and $21$ .

Factor $7$ out of $7 b (1 - 2 b)$ .

$\frac{7 (b (1 - 2 b))}{21 b (2 b - 1)}$

Cancel the common factors.

Factor $7$ out of $21 b (2 b - 1)$ .

$\frac{7 (b (1 - 2 b))}{7 (3 b (2 b - 1))}$

Cancel the common factor.

$\frac{7 (b (1 - 2 b))}{7 (3 b (2 b - 1))}$

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $b$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Step 5

Cancel the common factor of $1 - 2 b$ and $2 b - 1$ .

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

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

Factor $- 1$ out of $- 2 b$ .

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

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

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

Reorder terms.

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{3}$

$\frac{- 1}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$

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