What is ((a^2b-b^3))/((2ab-2b^2)) ?

The solution to ((a^2b-b^3))/((2ab-2b^2)) is (a+b)/2

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simplify ((a^2b-b^3))/((2ab-2b^2))

simplify

\frac{( a ^{2} b - b ^{3} )}{( 2 ab - 2 b ^{2} )}

\frac{a + b}{2}

Solution steps

\frac{a ^{2} b - b ^{3}}{2 ab - 2 b ^{2}}

Factor

a^{2} b - b^{3} : b (a + b) (a - b)

= \frac{b ( a + b ) ( a - b )}{2 ab - 2 b ^{2}}

Factor

2 ab - 2 b^{2} : 2 b (a - b)

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

Cancel the common factor:

b

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

Cancel the common factor:

a - b

= \frac{a + b}{2}

(6 x^{2} + 7 x + 2) - (- 9 x^{2} - 10)

\frac{6 x + 2}{x ^{3} - 2 x - 7}

2 \frac{1}{5}

(- 4 x^{2} + 3 x + 3) - (4 x^{2} + 9)

\frac{x ^{2} + 2 x + 1}{x ^{2} - 1}

What is ((a^2b-b^3))/((2ab-2b^2)) ?
The solution to ((a^2b-b^3))/((2ab-2b^2)) is (a+b)/2