Solve 5x+25/x^2-4x-45-9/x-9

$$\frac { 5 x + 25 } { x ^ { 2 } - 4 x - 45 } - \frac { 9 } { x - 9 }$$

Evaluate

$$-\frac{4}{x-9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5x+25}{x^{2}-4x-45}.

$$\frac{5\left(x+5\right)}{\left(x-9\right)\left(x+5\right)}-\frac{9}{x-9}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{5}{x-9}-\frac{9}{x-9}$$

Since \frac{5}{x-9} and \frac{9}{x-9} have the same denominator, subtract them by subtracting their numerators. Subtract 9 from 5 to get -4.

$$\frac{-4}{x-9}$$

Expand

$$-\frac{4}{x-9}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{5x+25}{x^{2}-4x-45}.

$$\frac{5\left(x+5\right)}{\left(x-9\right)\left(x+5\right)}-\frac{9}{x-9}$$

Cancel out x+5 in both numerator and denominator.

$$\frac{5}{x-9}-\frac{9}{x-9}$$

Since \frac{5}{x-9} and \frac{9}{x-9} have the same denominator, subtract them by subtracting their numerators. Subtract 9 from 5 to get -4.

$$\frac{-4}{x-9}$$