Solve c/c-10-c+1/4c-40+3/c

$$\frac { c } { c - 10 } - \frac { c + 1 } { 4 c - 40 } + \frac { 3 } { c }$$

Evaluate

$$\frac{3c^{2}+11c-120}{4c\left(c-10\right)}$$

Short Solution Steps

Factor 4c-40.

$$\frac{c}{c-10}-\frac{c+1}{4\left(c-10\right)}+\frac{3}{c}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c-10 and 4\left(c-10\right) is 4\left(c-10\right). Multiply \frac{c}{c-10} times \frac{4}{4}.

$$\frac{4c}{4\left(c-10\right)}-\frac{c+1}{4\left(c-10\right)}+\frac{3}{c}$$

Since \frac{4c}{4\left(c-10\right)} and \frac{c+1}{4\left(c-10\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4c-\left(c+1\right)}{4\left(c-10\right)}+\frac{3}{c}$$

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

$$\frac{4c-c-1}{4\left(c-10\right)}+\frac{3}{c}$$

Combine like terms in 4c-c-1.

$$\frac{3c-1}{4\left(c-10\right)}+\frac{3}{c}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(c-10\right) and c is 4c\left(c-10\right). Multiply \frac{3c-1}{4\left(c-10\right)} times \frac{c}{c}. Multiply \frac{3}{c} times \frac{4\left(c-10\right)}{4\left(c-10\right)}.

$$\frac{\left(3c-1\right)c}{4c\left(c-10\right)}+\frac{3\times 4\left(c-10\right)}{4c\left(c-10\right)}$$

Since \frac{\left(3c-1\right)c}{4c\left(c-10\right)} and \frac{3\times 4\left(c-10\right)}{4c\left(c-10\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(3c-1\right)c+3\times 4\left(c-10\right)}{4c\left(c-10\right)}$$

Do the multiplications in \left(3c-1\right)c+3\times 4\left(c-10\right).

$$\frac{3c^{2}-c+12c-120}{4c\left(c-10\right)}$$

Combine like terms in 3c^{2}-c+12c-120.

$$\frac{3c^{2}+11c-120}{4c\left(c-10\right)}$$

Expand 4c\left(c-10\right).

$$\frac{3c^{2}+11c-120}{4c^{2}-40c}$$

Expand

$$\frac{3c^{2}+11c-120}{4c\left(c-10\right)}$$

Short Solution Steps

Factor 4c-40.

$$\frac{c}{c-10}-\frac{c+1}{4\left(c-10\right)}+\frac{3}{c}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of c-10 and 4\left(c-10\right) is 4\left(c-10\right). Multiply \frac{c}{c-10} times \frac{4}{4}.

$$\frac{4c}{4\left(c-10\right)}-\frac{c+1}{4\left(c-10\right)}+\frac{3}{c}$$

Since \frac{4c}{4\left(c-10\right)} and \frac{c+1}{4\left(c-10\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4c-\left(c+1\right)}{4\left(c-10\right)}+\frac{3}{c}$$

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

$$\frac{4c-c-1}{4\left(c-10\right)}+\frac{3}{c}$$

Combine like terms in 4c-c-1.

$$\frac{3c-1}{4\left(c-10\right)}+\frac{3}{c}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4\left(c-10\right) and c is 4c\left(c-10\right). Multiply \frac{3c-1}{4\left(c-10\right)} times \frac{c}{c}. Multiply \frac{3}{c} times \frac{4\left(c-10\right)}{4\left(c-10\right)}.

$$\frac{\left(3c-1\right)c}{4c\left(c-10\right)}+\frac{3\times 4\left(c-10\right)}{4c\left(c-10\right)}$$

Since \frac{\left(3c-1\right)c}{4c\left(c-10\right)} and \frac{3\times 4\left(c-10\right)}{4c\left(c-10\right)} have the same denominator, add them by adding their numerators.

$$\frac{\left(3c-1\right)c+3\times 4\left(c-10\right)}{4c\left(c-10\right)}$$

Do the multiplications in \left(3c-1\right)c+3\times 4\left(c-10\right).

$$\frac{3c^{2}-c+12c-120}{4c\left(c-10\right)}$$

Combine like terms in 3c^{2}-c+12c-120.

$$\frac{3c^{2}+11c-120}{4c\left(c-10\right)}$$

Expand 4c\left(c-10\right).

$$\frac{3c^{2}+11c-120}{4c^{2}-40c}$$