Solve 4k+23/k^2-15k-k^2+6k/k^2-15k

$$\frac { 4 k + 23 } { k ^ { 2 } - 15 k } - \frac { k ^ { 2 } + 6 k } { k ^ { 2 } - 15 k }$$

Evaluate

$$\frac{23-2k-k^{2}}{k\left(k-15\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+6k}{k^{2}-15k}.

$$\frac{4k+23}{k^{2}-15k}-\frac{k\left(k+6\right)}{k\left(k-15\right)}$$

Cancel out k in both numerator and denominator.

$$\frac{4k+23}{k^{2}-15k}-\frac{k+6}{k-15}$$

Factor k^{2}-15k.

$$\frac{4k+23}{k\left(k-15\right)}-\frac{k+6}{k-15}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of k\left(k-15\right) and k-15 is k\left(k-15\right). Multiply \frac{k+6}{k-15} times \frac{k}{k}.

$$\frac{4k+23}{k\left(k-15\right)}-\frac{\left(k+6\right)k}{k\left(k-15\right)}$$

Since \frac{4k+23}{k\left(k-15\right)} and \frac{\left(k+6\right)k}{k\left(k-15\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4k+23-\left(k+6\right)k}{k\left(k-15\right)}$$

Do the multiplications in 4k+23-\left(k+6\right)k.

$$\frac{4k+23-k^{2}-6k}{k\left(k-15\right)}$$

Combine like terms in 4k+23-k^{2}-6k.

$$\frac{-2k+23-k^{2}}{k\left(k-15\right)}$$

Expand k\left(k-15\right).

$$\frac{-2k+23-k^{2}}{k^{2}-15k}$$

Expand

$$\frac{23-2k-k^{2}}{k\left(k-15\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{k^{2}+6k}{k^{2}-15k}.

$$\frac{4k+23}{k^{2}-15k}-\frac{k\left(k+6\right)}{k\left(k-15\right)}$$

Cancel out k in both numerator and denominator.

$$\frac{4k+23}{k^{2}-15k}-\frac{k+6}{k-15}$$

Factor k^{2}-15k.

$$\frac{4k+23}{k\left(k-15\right)}-\frac{k+6}{k-15}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of k\left(k-15\right) and k-15 is k\left(k-15\right). Multiply \frac{k+6}{k-15} times \frac{k}{k}.

$$\frac{4k+23}{k\left(k-15\right)}-\frac{\left(k+6\right)k}{k\left(k-15\right)}$$

Since \frac{4k+23}{k\left(k-15\right)} and \frac{\left(k+6\right)k}{k\left(k-15\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4k+23-\left(k+6\right)k}{k\left(k-15\right)}$$

Do the multiplications in 4k+23-\left(k+6\right)k.

$$\frac{4k+23-k^{2}-6k}{k\left(k-15\right)}$$

Combine like terms in 4k+23-k^{2}-6k.

$$\frac{-2k+23-k^{2}}{k\left(k-15\right)}$$

Expand k\left(k-15\right).

$$\frac{-2k+23-k^{2}}{k^{2}-15k}$$