Solve 25/a-a/5+a

$$\frac { \frac { 25 } { a } - a } { 5 + a }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a}{a}.

$$\frac{\frac{25}{a}-\frac{aa}{a}}{5+a}$$

Since \frac{25}{a} and \frac{aa}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-aa}{a}}{5+a}$$

Do the multiplications in 25-aa.

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

Express \frac{\frac{25-a^{2}}{a}}{5+a} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -5-a.

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

Cancel out a+5 in both numerator and denominator.

$$\frac{-\left(a-5\right)}{a}$$

Expand the expression.

$$\frac{-a+5}{a}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a times \frac{a}{a}.

$$\frac{\frac{25}{a}-\frac{aa}{a}}{5+a}$$

Since \frac{25}{a} and \frac{aa}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{25-aa}{a}}{5+a}$$

Do the multiplications in 25-aa.

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

Express \frac{\frac{25-a^{2}}{a}}{5+a} as a single fraction.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in -5-a.

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

Cancel out a+5 in both numerator and denominator.

$$\frac{-\left(a-5\right)}{a}$$

Expand the expression.

$$\frac{-a+5}{a}$$