Solve a-9/a/frac{9{a}+a}

$$\frac { a - \frac { 9 } { a } } { \frac { 9 } { a } + a }$$

Evaluate

$$\frac{a^{2}-9}{a^{2}+9}$$

Short Solution Steps

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

$$\frac{\frac{aa}{a}-\frac{9}{a}}{\frac{9}{a}+a}$$

Since \frac{aa}{a} and \frac{9}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{aa-9}{a}}{\frac{9}{a}+a}$$

Do the multiplications in aa-9.

$$\frac{\frac{a^{2}-9}{a}}{\frac{9}{a}+a}$$

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

$$\frac{\frac{a^{2}-9}{a}}{\frac{9}{a}+\frac{aa}{a}}$$

Since \frac{9}{a} and \frac{aa}{a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a^{2}-9}{a}}{\frac{9+aa}{a}}$$

Do the multiplications in 9+aa.

$$\frac{\frac{a^{2}-9}{a}}{\frac{9+a^{2}}{a}}$$

Divide \frac{a^{2}-9}{a} by \frac{9+a^{2}}{a} by multiplying \frac{a^{2}-9}{a} by the reciprocal of \frac{9+a^{2}}{a}.

$$\frac{\left(a^{2}-9\right)a}{a\left(9+a^{2}\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{2}-9}{a^{2}+9}$$

Expand

$$\frac{a^{2}-9}{a^{2}+9}$$

Short Solution Steps

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

$$\frac{\frac{aa}{a}-\frac{9}{a}}{\frac{9}{a}+a}$$

Since \frac{aa}{a} and \frac{9}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{aa-9}{a}}{\frac{9}{a}+a}$$

Do the multiplications in aa-9.

$$\frac{\frac{a^{2}-9}{a}}{\frac{9}{a}+a}$$

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

$$\frac{\frac{a^{2}-9}{a}}{\frac{9}{a}+\frac{aa}{a}}$$

Since \frac{9}{a} and \frac{aa}{a} have the same denominator, add them by adding their numerators.

$$\frac{\frac{a^{2}-9}{a}}{\frac{9+aa}{a}}$$

Do the multiplications in 9+aa.

$$\frac{\frac{a^{2}-9}{a}}{\frac{9+a^{2}}{a}}$$

Divide \frac{a^{2}-9}{a} by \frac{9+a^{2}}{a} by multiplying \frac{a^{2}-9}{a} by the reciprocal of \frac{9+a^{2}}{a}.

$$\frac{\left(a^{2}-9\right)a}{a\left(9+a^{2}\right)}$$

Cancel out a in both numerator and denominator.

$$\frac{a^{2}-9}{a^{2}+9}$$