Solve frac{x^{2}}{5x^2-25}-1/5-x^3+x^2/(x+1)(5x^2-25)

$$\frac { x ^ { 2 } } { 5 x ^ { 2 } - 25 } - \frac { 1 } { 5 } - \frac { x ^ { 3 } + x ^ { 2 } } { ( x + 1 ) ( 5 x ^ { 2 } - 25 ) }$$

Evaluate

$$-\frac{1}{5}=-0.2$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{3}+x^{2}}{\left(x+1\right)\left(5x^{2}-25\right)}.

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

Cancel out x+1 in both numerator and denominator.

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

Factor 5x^{2}-25.

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

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

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

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

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

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

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

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

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

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

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

Extract the negative sign in 5-x^{2}.

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

Cancel out x^{2}-5 in both numerator and denominator.

$$\frac{-1}{5}$$

Fraction \frac{-1}{5} can be rewritten as -\frac{1}{5} by extracting the negative sign.

$$-\frac{1}{5}$$

Factor

$$-\frac{1}{5} = -0.2$$