Solve a^2c/a^2b+b^3-c/b

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

Evaluate

$$-\frac{bc}{a^{2}+b^{2}}$$

Short Solution Steps

Factor a^{2}b+b^{3}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b\left(a^{2}+b^{2}\right) and b is b\left(a^{2}+b^{2}\right). Multiply \frac{c}{b} times \frac{a^{2}+b^{2}}{a^{2}+b^{2}}.

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

Since \frac{a^{2}c}{b\left(a^{2}+b^{2}\right)} and \frac{c\left(a^{2}+b^{2}\right)}{b\left(a^{2}+b^{2}\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in a^{2}c-c\left(a^{2}+b^{2}\right).

$$\frac{a^{2}c-ca^{2}-cb^{2}}{b\left(a^{2}+b^{2}\right)}$$

Combine like terms in a^{2}c-ca^{2}-cb^{2}.

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

Cancel out b in both numerator and denominator.

$$\frac{-bc}{a^{2}+b^{2}}$$

Factor

$$-\frac{bc}{a^{2}+b^{2}}$$