Solve 4/2(a-4b)+8b^2/a(a-4b)

$$\frac { 4 } { 2 ( a - 4 b ) } + \frac { 8 b ^ { 2 } } { a ( a - 4 b ) }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(a-4b\right) and a\left(a-4b\right) is 2a\left(a-4b\right). Multiply \frac{4}{2\left(a-4b\right)} times \frac{a}{a}. Multiply \frac{8b^{2}}{a\left(a-4b\right)} times \frac{2}{2}.

$$\frac{4a}{2a\left(a-4b\right)}+\frac{2\times 8b^{2}}{2a\left(a-4b\right)}$$

Since \frac{4a}{2a\left(a-4b\right)} and \frac{2\times 8b^{2}}{2a\left(a-4b\right)} have the same denominator, add them by adding their numerators.

$$\frac{4a+2\times 8b^{2}}{2a\left(a-4b\right)}$$

Do the multiplications in 4a+2\times 8b^{2}.

$$\frac{4a+16b^{2}}{2a\left(a-4b\right)}$$

Factor the expressions that are not already factored in \frac{4a+16b^{2}}{2a\left(a-4b\right)}.

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

Cancel out 2 in both numerator and denominator.

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

Expand a\left(a-4b\right).

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

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

$$\frac{2a+8b^{2}}{a^{2}-4ab}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(a-4b\right) and a\left(a-4b\right) is 2a\left(a-4b\right). Multiply \frac{4}{2\left(a-4b\right)} times \frac{a}{a}. Multiply \frac{8b^{2}}{a\left(a-4b\right)} times \frac{2}{2}.

$$\frac{4a}{2a\left(a-4b\right)}+\frac{2\times 8b^{2}}{2a\left(a-4b\right)}$$

Since \frac{4a}{2a\left(a-4b\right)} and \frac{2\times 8b^{2}}{2a\left(a-4b\right)} have the same denominator, add them by adding their numerators.

$$\frac{4a+2\times 8b^{2}}{2a\left(a-4b\right)}$$

Do the multiplications in 4a+2\times 8b^{2}.

$$\frac{4a+16b^{2}}{2a\left(a-4b\right)}$$

Factor the expressions that are not already factored in \frac{4a+16b^{2}}{2a\left(a-4b\right)}.

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

Cancel out 2 in both numerator and denominator.

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

Expand a\left(a-4b\right).

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

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

$$\frac{2a+8b^{2}}{a^{2}-4ab}$$