Solve ableft(a+bright)/(a-b)*4c^24c^2/a^2+ab

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

Evaluate

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

Short Solution Steps

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

$$\frac{ba^{2}+ab^{2}}{\left(a-b\right)\times 4c^{2}}\times \frac{4c^{2}}{a^{2}+ab}$$

Use the distributive property to multiply a-b by 4.

$$\frac{ba^{2}+ab^{2}}{\left(4a-4b\right)c^{2}}\times \frac{4c^{2}}{a^{2}+ab}$$

Use the distributive property to multiply 4a-4b by c^{2}.

$$\frac{ba^{2}+ab^{2}}{4ac^{2}-4bc^{2}}\times \frac{4c^{2}}{a^{2}+ab}$$

Multiply \frac{ba^{2}+ab^{2}}{4ac^{2}-4bc^{2}} times \frac{4c^{2}}{a^{2}+ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(ba^{2}+ab^{2}\right)\times 4c^{2}}{\left(4ac^{2}-4bc^{2}\right)\left(a^{2}+ab\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4a\left(a+b\right)c^{2} in both numerator and denominator.

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

Expand

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

Short Solution Steps

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

$$\frac{ba^{2}+ab^{2}}{\left(a-b\right)\times 4c^{2}}\times \frac{4c^{2}}{a^{2}+ab}$$

Use the distributive property to multiply a-b by 4.

$$\frac{ba^{2}+ab^{2}}{\left(4a-4b\right)c^{2}}\times \frac{4c^{2}}{a^{2}+ab}$$

Use the distributive property to multiply 4a-4b by c^{2}.

$$\frac{ba^{2}+ab^{2}}{4ac^{2}-4bc^{2}}\times \frac{4c^{2}}{a^{2}+ab}$$

Multiply \frac{ba^{2}+ab^{2}}{4ac^{2}-4bc^{2}} times \frac{4c^{2}}{a^{2}+ab} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(ba^{2}+ab^{2}\right)\times 4c^{2}}{\left(4ac^{2}-4bc^{2}\right)\left(a^{2}+ab\right)}$$

Factor the expressions that are not already factored.

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

Cancel out 4a\left(a+b\right)c^{2} in both numerator and denominator.

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