Solve 3a/a+2b:b-a/b

$$\frac { 3 a } { a + 2 b } : \frac { b - a } { b }$$

Evaluate

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

Short Solution Steps

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

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

Apply the distributive property by multiplying each term of a+2b by each term of b-a.

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

Combine ab and -2ba to get -ab.

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

Expand

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

Short Solution Steps

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

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

Apply the distributive property by multiplying each term of a+2b by each term of b-a.

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

Combine ab and -2ba to get -ab.

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