What is b/(2b+1)-(2b)/(b-2) ?

The solution to b/(2b+1)-(2b)/(b-2) is (-3b^2-4b)/((b-2)(2b+1))

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simplify b/(2b+1)-(2b)/(b-2)

simplify

\frac{b}{2 b + 1} - \frac{2 b}{b - 2}

\frac{- 3 b ^{2} - 4 b}{( b - 2 ) ( 2 b + 1 )}

Solution steps

\frac{b}{2 b + 1} - \frac{2 b}{b - 2}

Least Common Multiplier of

2 b + 1, b - 2 : (b - 2) (2 b + 1)

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

b (b - 2) - 2 b (2 b + 1) : - 3 b^{2} - 4 b

= \frac{- 3 b ^{2} - 4 b}{( b - 2 ) ( 2 b + 1 )}

(6^{- 1})^{- 2}

(5 x - 3) (25 x^{2} + 15 x + 9)

(x + 4)^{2}

\frac{6 + 2}{2}

\frac{z}{z}

What is b/(2b+1)-(2b)/(b-2) ?
The solution to b/(2b+1)-(2b)/(b-2) is (-3b^2-4b)/((b-2)(2b+1))