Solve x/x+6-2x/25

$$\frac { x } { x + 6 } - \frac { 2 x } { 25 }$$

Evaluate

$$\frac{x\left(13-2x\right)}{25\left(x+6\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+6 and 25 is 25\left(x+6\right). Multiply \frac{x}{x+6} times \frac{25}{25}. Multiply \frac{2x}{25} times \frac{x+6}{x+6}.

$$\frac{25x}{25\left(x+6\right)}-\frac{2x\left(x+6\right)}{25\left(x+6\right)}$$

Since \frac{25x}{25\left(x+6\right)} and \frac{2x\left(x+6\right)}{25\left(x+6\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25x-2x\left(x+6\right)}{25\left(x+6\right)}$$

Do the multiplications in 25x-2x\left(x+6\right).

$$\frac{25x-2x^{2}-12x}{25\left(x+6\right)}$$

Combine like terms in 25x-2x^{2}-12x.

$$\frac{13x-2x^{2}}{25\left(x+6\right)}$$

Expand 25\left(x+6\right).

$$\frac{13x-2x^{2}}{25x+150}$$

Factor

$$\frac{x\left(13-2x\right)}{25\left(x+6\right)}$$