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

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

Evaluate

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

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

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

Since \frac{aa}{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.

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

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

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

Expand 2a\left(a-4b\right).

$$\frac{a^{2}+16b^{2}}{2a^{2}-8ab}$$

Expand

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

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

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

Since \frac{aa}{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.

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

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

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

Expand 2a\left(a-4b\right).

$$\frac{a^{2}+16b^{2}}{2a^{2}-8ab}$$