Solve 7/5x-25+x+7/x-5

$$\frac { 7 } { 5 x - 25 } + \frac { x + 7 } { x - 5 }$$

Evaluate

$$\frac{5x+42}{5\left(x-5\right)}$$

Short Solution Steps

Factor 5x-25.

$$\frac{7}{5\left(x-5\right)}+\frac{x+7}{x-5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(x-5\right) and x-5 is 5\left(x-5\right). Multiply \frac{x+7}{x-5} times \frac{5}{5}.

$$\frac{7}{5\left(x-5\right)}+\frac{5\left(x+7\right)}{5\left(x-5\right)}$$

Since \frac{7}{5\left(x-5\right)} and \frac{5\left(x+7\right)}{5\left(x-5\right)} have the same denominator, add them by adding their numerators.

$$\frac{7+5\left(x+7\right)}{5\left(x-5\right)}$$

Do the multiplications in 7+5\left(x+7\right).

$$\frac{7+5x+35}{5\left(x-5\right)}$$

Combine like terms in 7+5x+35.

$$\frac{42+5x}{5\left(x-5\right)}$$

Expand 5\left(x-5\right).

$$\frac{42+5x}{5x-25}$$

Expand

$$\frac{5x+42}{5\left(x-5\right)}$$

Short Solution Steps

Factor 5x-25.

$$\frac{7}{5\left(x-5\right)}+\frac{x+7}{x-5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5\left(x-5\right) and x-5 is 5\left(x-5\right). Multiply \frac{x+7}{x-5} times \frac{5}{5}.

$$\frac{7}{5\left(x-5\right)}+\frac{5\left(x+7\right)}{5\left(x-5\right)}$$

Since \frac{7}{5\left(x-5\right)} and \frac{5\left(x+7\right)}{5\left(x-5\right)} have the same denominator, add them by adding their numerators.

$$\frac{7+5\left(x+7\right)}{5\left(x-5\right)}$$

Do the multiplications in 7+5\left(x+7\right).

$$\frac{7+5x+35}{5\left(x-5\right)}$$

Combine like terms in 7+5x+35.

$$\frac{42+5x}{5\left(x-5\right)}$$

Expand 5\left(x-5\right).

$$\frac{42+5x}{5x-25}$$