Solve +mathfrak{H}*frac{a^{4}-a^{2}b^2}{(a-b)^2}diva(a+b)/b^2*b^2/a=

$$+ \mathfrak { H } \cdot \frac { a ^ { 4 } - a ^ { 2 } b ^ { 2 } } { ( a - b ) ^ { 2 } } \div \frac { a ( a + b ) } { b ^ { 2 } } \cdot \frac { b ^ { 2 } } { a } =$$

Evaluate

$$\frac{Hb^{4}}{a-b}$$

$$a\neq 0\text{ and }b\neq 0\text{ and }|a|\neq |b|$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{4}-a^{2}b^{2}}{\left(a-b\right)^{2}}.

$$\frac{H\times \frac{\left(a+b\right)\left(a-b\right)a^{2}}{\left(a-b\right)^{2}}}{\frac{a\left(a+b\right)}{b^{2}}}\times \frac{b^{2}}{a}$$

Cancel out a-b in both numerator and denominator.

$$\frac{H\times \frac{\left(a+b\right)a^{2}}{a-b}}{\frac{a\left(a+b\right)}{b^{2}}}\times \frac{b^{2}}{a}$$

Express H\times \frac{\left(a+b\right)a^{2}}{a-b} as a single fraction.

$$\frac{\frac{H\left(a+b\right)a^{2}}{a-b}}{\frac{a\left(a+b\right)}{b^{2}}}\times \frac{b^{2}}{a}$$

Divide \frac{H\left(a+b\right)a^{2}}{a-b} by \frac{a\left(a+b\right)}{b^{2}} by multiplying \frac{H\left(a+b\right)a^{2}}{a-b} by the reciprocal of \frac{a\left(a+b\right)}{b^{2}}.

$$\frac{H\left(a+b\right)a^{2}b^{2}}{\left(a-b\right)a\left(a+b\right)}\times \frac{b^{2}}{a}$$

Cancel out a\left(a+b\right) in both numerator and denominator.

$$\frac{Hab^{2}}{a-b}\times \frac{b^{2}}{a}$$

Multiply \frac{Hab^{2}}{a-b} times \frac{b^{2}}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{Hab^{2}b^{2}}{\left(a-b\right)a}$$

Cancel out a in both numerator and denominator.

$$\frac{Hb^{2}b^{2}}{a-b}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{Hb^{4}}{a-b}$$

Expand

$$-\frac{Hb^{4}}{b-a}$$

$$a\neq 0\text{ and }b\neq 0\text{ and }|a|\neq |b|$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{4}-a^{2}b^{2}}{\left(a-b\right)^{2}}.

$$\frac{H\times \frac{\left(a+b\right)\left(a-b\right)a^{2}}{\left(a-b\right)^{2}}}{\frac{a\left(a+b\right)}{b^{2}}}\times \frac{b^{2}}{a}$$

Cancel out a-b in both numerator and denominator.

$$\frac{H\times \frac{\left(a+b\right)a^{2}}{a-b}}{\frac{a\left(a+b\right)}{b^{2}}}\times \frac{b^{2}}{a}$$

Express H\times \frac{\left(a+b\right)a^{2}}{a-b} as a single fraction.

$$\frac{\frac{H\left(a+b\right)a^{2}}{a-b}}{\frac{a\left(a+b\right)}{b^{2}}}\times \frac{b^{2}}{a}$$

Divide \frac{H\left(a+b\right)a^{2}}{a-b} by \frac{a\left(a+b\right)}{b^{2}} by multiplying \frac{H\left(a+b\right)a^{2}}{a-b} by the reciprocal of \frac{a\left(a+b\right)}{b^{2}}.

$$\frac{H\left(a+b\right)a^{2}b^{2}}{\left(a-b\right)a\left(a+b\right)}\times \frac{b^{2}}{a}$$

Cancel out a\left(a+b\right) in both numerator and denominator.

$$\frac{Hab^{2}}{a-b}\times \frac{b^{2}}{a}$$

Multiply \frac{Hab^{2}}{a-b} times \frac{b^{2}}{a} by multiplying numerator times numerator and denominator times denominator.

$$\frac{Hab^{2}b^{2}}{\left(a-b\right)a}$$

Cancel out a in both numerator and denominator.

$$\frac{Hb^{2}b^{2}}{a-b}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{Hb^{4}}{a-b}$$