Solve (x-9+-x^2-25/2x+5)*(2x+5)

$$(x-9+ \frac{ - { x }^{ 2 } -25 }{ 2x+5 } ) \times (2x+5)$$

Evaluate

$$x^{2}-13x-70$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-9 times \frac{2x+5}{2x+5}.

$$\left(\frac{\left(x-9\right)\left(2x+5\right)}{2x+5}+\frac{-x^{2}-25}{2x+5}\right)\left(2x+5\right)$$

Since \frac{\left(x-9\right)\left(2x+5\right)}{2x+5} and \frac{-x^{2}-25}{2x+5} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-9\right)\left(2x+5\right)-x^{2}-25}{2x+5}\left(2x+5\right)$$

Do the multiplications in \left(x-9\right)\left(2x+5\right)-x^{2}-25.

$$\frac{2x^{2}+5x-18x-45-x^{2}-25}{2x+5}\left(2x+5\right)$$

Combine like terms in 2x^{2}+5x-18x-45-x^{2}-25.

$$\frac{x^{2}-13x-70}{2x+5}\left(2x+5\right)$$

Cancel out 2x+5 and 2x+5.

$$x^{2}-13x-70$$

Expand

$$x^{2}-13x-70$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply x-9 times \frac{2x+5}{2x+5}.

$$\left(\frac{\left(x-9\right)\left(2x+5\right)}{2x+5}+\frac{-x^{2}-25}{2x+5}\right)\left(2x+5\right)$$

Since \frac{\left(x-9\right)\left(2x+5\right)}{2x+5} and \frac{-x^{2}-25}{2x+5} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-9\right)\left(2x+5\right)-x^{2}-25}{2x+5}\left(2x+5\right)$$

Do the multiplications in \left(x-9\right)\left(2x+5\right)-x^{2}-25.

$$\frac{2x^{2}+5x-18x-45-x^{2}-25}{2x+5}\left(2x+5\right)$$

Combine like terms in 2x^{2}+5x-18x-45-x^{2}-25.

$$\frac{x^{2}-13x-70}{2x+5}\left(2x+5\right)$$

Cancel out 2x+5 and 2x+5.

$$x^{2}-13x-70$$