Solve 2B(a+B)/a*(a-b):b+a/b-a

$$\frac { 2 B ( a + B ) } { a \cdot ( a - b ) } : \frac { b + a } { b - a }$$

Evaluate

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

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

Short Solution Steps

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

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

Extract the negative sign in b-a.

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

Cancel out a-b in both numerator and denominator.

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

Use the distributive property to multiply -2B by B+a.

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

Use the distributive property to multiply a by a+b.

$$\frac{-2B^{2}-2Ba}{a^{2}+ab}$$

Expand

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

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

Short Solution Steps

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

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

Extract the negative sign in b-a.

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

Cancel out a-b in both numerator and denominator.

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

Use the distributive property to multiply -2B by B+a.

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

Use the distributive property to multiply a by a+b.

$$\frac{-2B^{2}-2Ba}{a^{2}+ab}$$