Solve 1-a-3/a+a^2-9/a^2+a

$$1 - \frac { a - 3 } { a } + \frac { a ^ { 2 } - 9 } { a ^ { 2 } + a }$$

Evaluate

$$\frac{a^{2}+3a-6}{a\left(a+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$\frac{a}{a}-\frac{a-3}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Since \frac{a}{a} and \frac{a-3}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-\left(a-3\right)}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Do the multiplications in a-\left(a-3\right).

$$\frac{a-a+3}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Combine like terms in a-a+3.

$$\frac{3}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Factor a^{2}+a.

$$\frac{3}{a}+\frac{a^{2}-9}{a\left(a+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and a\left(a+1\right) is a\left(a+1\right). Multiply \frac{3}{a} times \frac{a+1}{a+1}.

$$\frac{3\left(a+1\right)}{a\left(a+1\right)}+\frac{a^{2}-9}{a\left(a+1\right)}$$

Since \frac{3\left(a+1\right)}{a\left(a+1\right)} and \frac{a^{2}-9}{a\left(a+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+1\right)+a^{2}-9}{a\left(a+1\right)}$$

Do the multiplications in 3\left(a+1\right)+a^{2}-9.

$$\frac{3a+3+a^{2}-9}{a\left(a+1\right)}$$

Combine like terms in 3a+3+a^{2}-9.

$$\frac{3a-6+a^{2}}{a\left(a+1\right)}$$

Expand a\left(a+1\right).

$$\frac{3a-6+a^{2}}{a^{2}+a}$$

Expand

$$\frac{a^{2}+3a-6}{a\left(a+1\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$\frac{a}{a}-\frac{a-3}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Since \frac{a}{a} and \frac{a-3}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-\left(a-3\right)}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Do the multiplications in a-\left(a-3\right).

$$\frac{a-a+3}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Combine like terms in a-a+3.

$$\frac{3}{a}+\frac{a^{2}-9}{a^{2}+a}$$

Factor a^{2}+a.

$$\frac{3}{a}+\frac{a^{2}-9}{a\left(a+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and a\left(a+1\right) is a\left(a+1\right). Multiply \frac{3}{a} times \frac{a+1}{a+1}.

$$\frac{3\left(a+1\right)}{a\left(a+1\right)}+\frac{a^{2}-9}{a\left(a+1\right)}$$

Since \frac{3\left(a+1\right)}{a\left(a+1\right)} and \frac{a^{2}-9}{a\left(a+1\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\left(a+1\right)+a^{2}-9}{a\left(a+1\right)}$$

Do the multiplications in 3\left(a+1\right)+a^{2}-9.

$$\frac{3a+3+a^{2}-9}{a\left(a+1\right)}$$

Combine like terms in 3a+3+a^{2}-9.

$$\frac{3a-6+a^{2}}{a\left(a+1\right)}$$

Expand a\left(a+1\right).

$$\frac{3a-6+a^{2}}{a^{2}+a}$$