Solve b/a-b+frac{b^{3}}{a^{3}-2a^{2}b+ab^2}divab+b^2/a^2-a^2

$$\frac { b } { a - b } + \frac { b ^ { 3 } } { a ^ { 3 } - 2 a ^ { 2 } b + a b ^ { 2 } } \div \frac { a b + b ^ { 2 } } { a ^ { 2 } - a ^ { 2 } }$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Divide \frac{b^{3}}{a^{3}-2a^{2}b+ab^{2}} by \frac{ab+b^{2}}{a^{2}-a^{2}} by multiplying \frac{b^{3}}{a^{3}-2a^{2}b+ab^{2}} by the reciprocal of \frac{ab+b^{2}}{a^{2}-a^{2}}.

$$\frac{b}{a-b}+\frac{b^{3}\left(a^{2}-a^{2}\right)}{\left(a^{3}-2a^{2}b+ab^{2}\right)\left(ab+b^{2}\right)}$$

Combine a^{2} and -a^{2} to get 0.

$$\frac{b}{a-b}+\frac{b^{3}\times 0}{\left(a^{3}-2a^{2}b+ab^{2}\right)\left(ab+b^{2}\right)}$$

Anything times zero gives zero.

$$\frac{b}{a-b}+\frac{0}{\left(a^{3}-2a^{2}b+ab^{2}\right)\left(ab+b^{2}\right)}$$

Zero divided by any non-zero term gives zero.

$$\frac{b}{a-b}+0$$

Anything plus zero gives itself.

$$\frac{b}{a-b}$$

Expand

$$\text{Indeterminate}$$

Solution Steps

Divide \frac{b^{3}}{a^{3}-2a^{2}b+ab^{2}} by \frac{ab+b^{2}}{a^{2}-a^{2}} by multiplying \frac{b^{3}}{a^{3}-2a^{2}b+ab^{2}} by the reciprocal of \frac{ab+b^{2}}{a^{2}-a^{2}}.

$$\frac{b}{a-b}+\frac{b^{3}\left(a^{2}-a^{2}\right)}{\left(a^{3}-2a^{2}b+ab^{2}\right)\left(ab+b^{2}\right)}$$

Combine a^{2} and -a^{2} to get 0.

$$\frac{b}{a-b}+\frac{b^{3}\times 0}{\left(a^{3}-2a^{2}b+ab^{2}\right)\left(ab+b^{2}\right)}$$

Anything times zero gives zero.

$$\frac{b}{a-b}+\frac{0}{\left(a^{3}-2a^{2}b+ab^{2}\right)\left(ab+b^{2}\right)}$$

Zero divided by any non-zero term gives zero.

$$\frac{b}{a-b}+0$$

Anything plus zero gives itself.

$$\frac{b}{a-b}$$