Solve -1/(x+5)^2-4

$$\frac { - 1 } { ( x + 5 ) ^ { 2 } } - 4$$

Evaluate

$$-\frac{4x^{2}+40x+101}{\left(x+5\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x+5\right)^{2}}{\left(x+5\right)^{2}}.

$$\frac{-1}{\left(x+5\right)^{2}}-\frac{4\left(x+5\right)^{2}}{\left(x+5\right)^{2}}$$

Since \frac{-1}{\left(x+5\right)^{2}} and \frac{4\left(x+5\right)^{2}}{\left(x+5\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-4\left(x+5\right)^{2}}{\left(x+5\right)^{2}}$$

Do the multiplications in -1-4\left(x+5\right)^{2}.

$$\frac{-1-4x^{2}-40x-100}{\left(x+5\right)^{2}}$$

Combine like terms in -1-4x^{2}-40x-100.

$$\frac{-101-4x^{2}-40x}{\left(x+5\right)^{2}}$$

Expand \left(x+5\right)^{2}.

$$\frac{-101-4x^{2}-40x}{x^{2}+10x+25}$$

Expand

$$-\frac{4x^{2}+40x+101}{\left(x+5\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{\left(x+5\right)^{2}}{\left(x+5\right)^{2}}.

$$\frac{-1}{\left(x+5\right)^{2}}-\frac{4\left(x+5\right)^{2}}{\left(x+5\right)^{2}}$$

Since \frac{-1}{\left(x+5\right)^{2}} and \frac{4\left(x+5\right)^{2}}{\left(x+5\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-4\left(x+5\right)^{2}}{\left(x+5\right)^{2}}$$

Do the multiplications in -1-4\left(x+5\right)^{2}.

$$\frac{-1-4x^{2}-40x-100}{\left(x+5\right)^{2}}$$

Combine like terms in -1-4x^{2}-40x-100.

$$\frac{-101-4x^{2}-40x}{\left(x+5\right)^{2}}$$

Expand \left(x+5\right)^{2}.

$$\frac{-101-4x^{2}-40x}{x^{2}+10x+25}$$