Solve a-3b-5b^3/a+b/a-2b-frac{4b^2{a+b}}=

$$\frac { a - 3 b - \frac { 5 b ^ { 3 } } { a + b } } { a - 2 b - \frac { 4 b ^ { 2 } } { a + b } } =$$

Evaluate

$$\frac{a^{2}-2ab-5b^{3}-3b^{2}}{\left(a-3b\right)\left(a+2b\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a-3b times \frac{a+b}{a+b}.

$$\frac{\frac{\left(a-3b\right)\left(a+b\right)}{a+b}-\frac{5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

Since \frac{\left(a-3b\right)\left(a+b\right)}{a+b} and \frac{5b^{3}}{a+b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(a-3b\right)\left(a+b\right)-5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

Do the multiplications in \left(a-3b\right)\left(a+b\right)-5b^{3}.

$$\frac{\frac{a^{2}+ab-3ba-3b^{2}-5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

Combine like terms in a^{2}+ab-3ba-3b^{2}-5b^{3}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a-2b times \frac{a+b}{a+b}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{\left(a-2b\right)\left(a+b\right)}{a+b}-\frac{4b^{2}}{a+b}}$$

Since \frac{\left(a-2b\right)\left(a+b\right)}{a+b} and \frac{4b^{2}}{a+b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{\left(a-2b\right)\left(a+b\right)-4b^{2}}{a+b}}$$

Do the multiplications in \left(a-2b\right)\left(a+b\right)-4b^{2}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{a^{2}+ab-2ba-2b^{2}-4b^{2}}{a+b}}$$

Combine like terms in a^{2}+ab-2ba-2b^{2}-4b^{2}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{a^{2}-6b^{2}-ab}{a+b}}$$

Divide \frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b} by \frac{a^{2}-6b^{2}-ab}{a+b} by multiplying \frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b} by the reciprocal of \frac{a^{2}-6b^{2}-ab}{a+b}.

$$\frac{\left(a^{2}-3b^{2}-2ab-5b^{3}\right)\left(a+b\right)}{\left(a+b\right)\left(a^{2}-6b^{2}-ab\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{a^{2}-2ab-5b^{3}-3b^{2}}{a^{2}-ab-6b^{2}}$$

Expand

$$\frac{a^{2}-2ab-5b^{3}-3b^{2}}{a^{2}-ab-6b^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a-3b times \frac{a+b}{a+b}.

$$\frac{\frac{\left(a-3b\right)\left(a+b\right)}{a+b}-\frac{5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

Since \frac{\left(a-3b\right)\left(a+b\right)}{a+b} and \frac{5b^{3}}{a+b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(a-3b\right)\left(a+b\right)-5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

Do the multiplications in \left(a-3b\right)\left(a+b\right)-5b^{3}.

$$\frac{\frac{a^{2}+ab-3ba-3b^{2}-5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

Combine like terms in a^{2}+ab-3ba-3b^{2}-5b^{3}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{a-2b-\frac{4b^{2}}{a+b}}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a-2b times \frac{a+b}{a+b}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{\left(a-2b\right)\left(a+b\right)}{a+b}-\frac{4b^{2}}{a+b}}$$

Since \frac{\left(a-2b\right)\left(a+b\right)}{a+b} and \frac{4b^{2}}{a+b} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{\left(a-2b\right)\left(a+b\right)-4b^{2}}{a+b}}$$

Do the multiplications in \left(a-2b\right)\left(a+b\right)-4b^{2}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{a^{2}+ab-2ba-2b^{2}-4b^{2}}{a+b}}$$

Combine like terms in a^{2}+ab-2ba-2b^{2}-4b^{2}.

$$\frac{\frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b}}{\frac{a^{2}-6b^{2}-ab}{a+b}}$$

Divide \frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b} by \frac{a^{2}-6b^{2}-ab}{a+b} by multiplying \frac{a^{2}-3b^{2}-2ab-5b^{3}}{a+b} by the reciprocal of \frac{a^{2}-6b^{2}-ab}{a+b}.

$$\frac{\left(a^{2}-3b^{2}-2ab-5b^{3}\right)\left(a+b\right)}{\left(a+b\right)\left(a^{2}-6b^{2}-ab\right)}$$

Cancel out a+b in both numerator and denominator.

$$\frac{a^{2}-2ab-5b^{3}-3b^{2}}{a^{2}-ab-6b^{2}}$$