Solve 1/x^2-25-1/(x+5)^2

$$\frac { 1 } { x ^ { 2 } - 25 } - \frac { 1 } { ( x + 5 ) ^ { 2 } }$$

Evaluate

$$\frac{10}{\left(x-5\right)\left(x+5\right)^{2}}$$

Short Solution Steps

Factor x^{2}-25.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and \left(x+5\right)^{2} is \left(x-5\right)\left(x+5\right)^{2}. Multiply \frac{1}{\left(x-5\right)\left(x+5\right)} times \frac{x+5}{x+5}. Multiply \frac{1}{\left(x+5\right)^{2}} times \frac{x-5}{x-5}.

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

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

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

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

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

Combine like terms in x+5-x+5.

$$\frac{10}{\left(x-5\right)\left(x+5\right)^{2}}$$

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

$$\frac{10}{x^{3}+5x^{2}-25x-125}$$

Expand

$$\frac{10}{\left(x-5\right)\left(x+5\right)^{2}}$$

Short Solution Steps

Factor x^{2}-25.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-5\right)\left(x+5\right) and \left(x+5\right)^{2} is \left(x-5\right)\left(x+5\right)^{2}. Multiply \frac{1}{\left(x-5\right)\left(x+5\right)} times \frac{x+5}{x+5}. Multiply \frac{1}{\left(x+5\right)^{2}} times \frac{x-5}{x-5}.

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

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

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

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

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

Combine like terms in x+5-x+5.

$$\frac{10}{\left(x-5\right)\left(x+5\right)^{2}}$$

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

$$\frac{10}{x^{3}+5x^{2}-25x-125}$$