What is (a^2-b^2)/(a^4b)*(ab^2)/(3a+3b) ?

The solution to (a^2-b^2)/(a^4b)*(ab^2)/(3a+3b) is ((a-b)b)/(3a^3)

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simplify (a^2-b^2)/(a^4b)*(ab^2)/(3a+3b)

simplify

\frac{a ^{2} - b ^{2}}{a ^{4} b} \cdot \frac{a b ^{2}}{3 a + 3 b}

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

Solution steps

\frac{a ^{2} - b ^{2}}{a ^{4} b} \cdot \frac{a b ^{2}}{3 a + 3 b}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

b^{2} = bb

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

Cancel the common factor:

b

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

a^{4} = a a^{3}

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

Cancel the common factor:

a

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

Apply Difference of Two Squares Formula:

x^{2} - y^{2} = (x + y) (x - y)

a^{2} - b^{2} = (a + b) (a - b)

= \frac{( a + b ) ( a - b ) b}{a ^{3} ( 3 a + 3 b )}

Factor out common term

3

= \frac{( a + b ) ( a - b ) b}{a ^{3} \cdot 3 ( a + b )}

Cancel the common factor:

a + b

= \frac{( a - b ) b}{a ^{3} \cdot 3}

= \frac{( a - b ) b}{3 a ^{3}}

40 \cdot \frac{π}{180}

0 < 1

3 a x - a y + 9 b x - 3 b y

\frac{15 !}{4 ! 11 !}

- x - 1 = x - 21

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