What is (7b-14b^2)/(42b^2-21b) ?

The solution to (7b-14b^2)/(42b^2-21b) is -1/3

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

simplify

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

- \frac{1}{3}

Decimal Notation

- 0.33333 \dots

Solution steps

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

Factor

7 b - 14 b^{2} : 7 b (1 - 2 b)

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

Factor

42 b^{2} - 21 b : 21 b (2 b - 1)

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

Cancel the common factor:

b

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

Factor the number:

21 = 7 \cdot 3

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

Cancel the common factor:

7

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

1 - 2 b = - (2 b - 1)

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

Cancel the common factor:

2 b - 1

= \frac{- 1}{3}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{3}

(- 2.3551 \cdot 1 0^{4}) \cdot \frac{1}{8.314} \cdot \frac{1}{285}

4 x + 1 = 0

4 b^{4} - 49 b^{2}

\frac{9}{7} \cdot 14

0.05 x^{2} = 1.73 x - 0.285 x^{2}