Solve 10/c-2-c+2/c-2-c+4/c-1

$$\frac { 10 } { c - 2 } - \frac { c + 2 } { c - 2 } - \frac { c + 4 } { c - 1 }$$

Evaluate

$$\frac{c\left(7-2c\right)}{\left(c-2\right)\left(c-1\right)}$$

Short Solution Steps

Since \frac{10}{c-2} and \frac{c+2}{c-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-\left(c+2\right)}{c-2}-\frac{c+4}{c-1}$$

Do the multiplications in 10-\left(c+2\right).

$$\frac{10-c-2}{c-2}-\frac{c+4}{c-1}$$

Combine like terms in 10-c-2.

$$\frac{8-c}{c-2}-\frac{c+4}{c-1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c-2 and c-1 is \left(c-2\right)\left(c-1\right). Multiply \frac{8-c}{c-2} times \frac{c-1}{c-1}. Multiply \frac{c+4}{c-1} times \frac{c-2}{c-2}.

$$\frac{\left(8-c\right)\left(c-1\right)}{\left(c-2\right)\left(c-1\right)}-\frac{\left(c+4\right)\left(c-2\right)}{\left(c-2\right)\left(c-1\right)}$$

Since \frac{\left(8-c\right)\left(c-1\right)}{\left(c-2\right)\left(c-1\right)} and \frac{\left(c+4\right)\left(c-2\right)}{\left(c-2\right)\left(c-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(8-c\right)\left(c-1\right)-\left(c+4\right)\left(c-2\right)}{\left(c-2\right)\left(c-1\right)}$$

Do the multiplications in \left(8-c\right)\left(c-1\right)-\left(c+4\right)\left(c-2\right).

$$\frac{8c-8-c^{2}+c-c^{2}+2c-4c+8}{\left(c-2\right)\left(c-1\right)}$$

Combine like terms in 8c-8-c^{2}+c-c^{2}+2c-4c+8.

$$\frac{7c-2c^{2}}{\left(c-2\right)\left(c-1\right)}$$

Expand \left(c-2\right)\left(c-1\right).

$$\frac{7c-2c^{2}}{c^{2}-3c+2}$$

Expand

$$\frac{7c-2c^{2}}{\left(c-2\right)\left(c-1\right)}$$

Short Solution Steps

Since \frac{10}{c-2} and \frac{c+2}{c-2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-\left(c+2\right)}{c-2}-\frac{c+4}{c-1}$$

Do the multiplications in 10-\left(c+2\right).

$$\frac{10-c-2}{c-2}-\frac{c+4}{c-1}$$

Combine like terms in 10-c-2.

$$\frac{8-c}{c-2}-\frac{c+4}{c-1}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c-2 and c-1 is \left(c-2\right)\left(c-1\right). Multiply \frac{8-c}{c-2} times \frac{c-1}{c-1}. Multiply \frac{c+4}{c-1} times \frac{c-2}{c-2}.

$$\frac{\left(8-c\right)\left(c-1\right)}{\left(c-2\right)\left(c-1\right)}-\frac{\left(c+4\right)\left(c-2\right)}{\left(c-2\right)\left(c-1\right)}$$

Since \frac{\left(8-c\right)\left(c-1\right)}{\left(c-2\right)\left(c-1\right)} and \frac{\left(c+4\right)\left(c-2\right)}{\left(c-2\right)\left(c-1\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(8-c\right)\left(c-1\right)-\left(c+4\right)\left(c-2\right)}{\left(c-2\right)\left(c-1\right)}$$

Do the multiplications in \left(8-c\right)\left(c-1\right)-\left(c+4\right)\left(c-2\right).

$$\frac{8c-8-c^{2}+c-c^{2}+2c-4c+8}{\left(c-2\right)\left(c-1\right)}$$

Combine like terms in 8c-8-c^{2}+c-c^{2}+2c-4c+8.

$$\frac{7c-2c^{2}}{\left(c-2\right)\left(c-1\right)}$$

Expand \left(c-2\right)\left(c-1\right).

$$\frac{7c-2c^{2}}{c^{2}-3c+2}$$