Solve c^2+c/c^2-25-c^2+5/c^2-25

$$\frac { c ^ { 2 } + c } { c ^ { 2 } - 25 } - \frac { c ^ { 2 } + 5 } { c ^ { 2 } - 25 }$$

Evaluate

$$\frac{1}{c+5}$$

Short Solution Steps

Since \frac{c^{2}+c}{c^{2}-25} and \frac{c^{2}+5}{c^{2}-25} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{c^{2}+c-c^{2}-5}{c^{2}-25}$$

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

$$\frac{c-5}{c^{2}-25}$$

Factor the expressions that are not already factored in \frac{c-5}{c^{2}-25}.

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

Cancel out c-5 in both numerator and denominator.

$$\frac{1}{c+5}$$

Expand

$$\frac{1}{c+5}$$

Short Solution Steps

Since \frac{c^{2}+c}{c^{2}-25} and \frac{c^{2}+5}{c^{2}-25} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{c^{2}+c-c^{2}-5}{c^{2}-25}$$

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

$$\frac{c-5}{c^{2}-25}$$

Factor the expressions that are not already factored in \frac{c-5}{c^{2}-25}.

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

Cancel out c-5 in both numerator and denominator.

$$\frac{1}{c+5}$$