Solve 4k+23/k^2-16k-k^2+4k/k^2-16k

$$\frac { 4 k + 23 } { k ^ { 2 } - 16 k } - \frac { k ^ { 2 } + 4 k } { k ^ { 2 } - 16 k }$$

Evaluate

$$\frac{23-k^{2}}{k\left(k-16\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+4k}{k^{2}-16k}.

$$\frac{4k+23}{k^{2}-16k}-\frac{k\left(k+4\right)}{k\left(k-16\right)}$$

Cancel out k in both numerator and denominator.

$$\frac{4k+23}{k^{2}-16k}-\frac{k+4}{k-16}$$

Factor k^{2}-16k.

$$\frac{4k+23}{k\left(k-16\right)}-\frac{k+4}{k-16}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of k\left(k-16\right) and k-16 is k\left(k-16\right). Multiply \frac{k+4}{k-16} times \frac{k}{k}.

$$\frac{4k+23}{k\left(k-16\right)}-\frac{\left(k+4\right)k}{k\left(k-16\right)}$$

Since \frac{4k+23}{k\left(k-16\right)} and \frac{\left(k+4\right)k}{k\left(k-16\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4k+23-\left(k+4\right)k}{k\left(k-16\right)}$$

Do the multiplications in 4k+23-\left(k+4\right)k.

$$\frac{4k+23-k^{2}-4k}{k\left(k-16\right)}$$

Combine like terms in 4k+23-k^{2}-4k.

$$\frac{23-k^{2}}{k\left(k-16\right)}$$

Expand k\left(k-16\right).

$$\frac{23-k^{2}}{k^{2}-16k}$$

Expand

$$\frac{23-k^{2}}{k\left(k-16\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+4k}{k^{2}-16k}.

$$\frac{4k+23}{k^{2}-16k}-\frac{k\left(k+4\right)}{k\left(k-16\right)}$$

Cancel out k in both numerator and denominator.

$$\frac{4k+23}{k^{2}-16k}-\frac{k+4}{k-16}$$

Factor k^{2}-16k.

$$\frac{4k+23}{k\left(k-16\right)}-\frac{k+4}{k-16}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of k\left(k-16\right) and k-16 is k\left(k-16\right). Multiply \frac{k+4}{k-16} times \frac{k}{k}.

$$\frac{4k+23}{k\left(k-16\right)}-\frac{\left(k+4\right)k}{k\left(k-16\right)}$$

Since \frac{4k+23}{k\left(k-16\right)} and \frac{\left(k+4\right)k}{k\left(k-16\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4k+23-\left(k+4\right)k}{k\left(k-16\right)}$$

Do the multiplications in 4k+23-\left(k+4\right)k.

$$\frac{4k+23-k^{2}-4k}{k\left(k-16\right)}$$

Combine like terms in 4k+23-k^{2}-4k.

$$\frac{23-k^{2}}{k\left(k-16\right)}$$

Expand k\left(k-16\right).

$$\frac{23-k^{2}}{k^{2}-16k}$$