Solve x-1/5x+2/25x-2+x/15x=

$$\frac { x - 1 } { 5 x } + \frac { 2 } { 25 x } - \frac { 2 + x } { 15 x } =$$

Evaluate

$$\frac{2}{15}-\frac{19}{75x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x and 25x is 25x. Multiply \frac{x-1}{5x} times \frac{5}{5}.

$$\frac{5\left(x-1\right)}{25x}+\frac{2}{25x}-\frac{2+x}{15x}$$

Since \frac{5\left(x-1\right)}{25x} and \frac{2}{25x} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x-1\right)+2}{25x}-\frac{2+x}{15x}$$

Do the multiplications in 5\left(x-1\right)+2.

$$\frac{5x-5+2}{25x}-\frac{2+x}{15x}$$

Combine like terms in 5x-5+2.

$$\frac{5x-3}{25x}-\frac{2+x}{15x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25x and 15x is 75x. Multiply \frac{5x-3}{25x} times \frac{3}{3}. Multiply \frac{2+x}{15x} times \frac{5}{5}.

$$\frac{3\left(5x-3\right)}{75x}-\frac{5\left(2+x\right)}{75x}$$

Since \frac{3\left(5x-3\right)}{75x} and \frac{5\left(2+x\right)}{75x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5x-3\right)-5\left(2+x\right)}{75x}$$

Do the multiplications in 3\left(5x-3\right)-5\left(2+x\right).

$$\frac{15x-9-10-5x}{75x}$$

Combine like terms in 15x-9-10-5x.

$$\frac{10x-19}{75x}$$

Expand

$$\frac{2}{15}-\frac{19}{75x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5x and 25x is 25x. Multiply \frac{x-1}{5x} times \frac{5}{5}.

$$\frac{5\left(x-1\right)}{25x}+\frac{2}{25x}-\frac{2+x}{15x}$$

Since \frac{5\left(x-1\right)}{25x} and \frac{2}{25x} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x-1\right)+2}{25x}-\frac{2+x}{15x}$$

Do the multiplications in 5\left(x-1\right)+2.

$$\frac{5x-5+2}{25x}-\frac{2+x}{15x}$$

Combine like terms in 5x-5+2.

$$\frac{5x-3}{25x}-\frac{2+x}{15x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 25x and 15x is 75x. Multiply \frac{5x-3}{25x} times \frac{3}{3}. Multiply \frac{2+x}{15x} times \frac{5}{5}.

$$\frac{3\left(5x-3\right)}{75x}-\frac{5\left(2+x\right)}{75x}$$

Since \frac{3\left(5x-3\right)}{75x} and \frac{5\left(2+x\right)}{75x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(5x-3\right)-5\left(2+x\right)}{75x}$$

Do the multiplications in 3\left(5x-3\right)-5\left(2+x\right).

$$\frac{15x-9-10-5x}{75x}$$

Combine like terms in 15x-9-10-5x.

$$\frac{10x-19}{75x}$$