Solve a^2+3/a^2-4-a^2-4/a^2-4=

$$\frac { a ^ { 2 } + 3 } { a ^ { 2 } - 4 } - \frac { a ^ { 2 } - 4 } { a ^ { 2 } - 4 } =$$

Evaluate

$$\frac{7}{a^{2}-4}$$

Short Solution Steps

Divide a^{2}-4 by a^{2}-4 to get 1.

$$\frac{a^{2}+3}{a^{2}-4}-1$$

Factor a^{2}-4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(a-2\right)\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}.

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

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

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

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

$$\frac{a^{2}+3-a^{2}-2a+2a+4}{\left(a-2\right)\left(a+2\right)}$$

Combine like terms in a^{2}+3-a^{2}-2a+2a+4.

$$\frac{7}{\left(a-2\right)\left(a+2\right)}$$

Expand \left(a-2\right)\left(a+2\right).

$$\frac{7}{a^{2}-4}$$

Expand

$$\frac{7}{a^{2}-4}$$

Short Solution Steps

Divide a^{2}-4 by a^{2}-4 to get 1.

$$\frac{a^{2}+3}{a^{2}-4}-1$$

Factor a^{2}-4.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(a-2\right)\left(a+2\right)}{\left(a-2\right)\left(a+2\right)}.

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

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

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

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

$$\frac{a^{2}+3-a^{2}-2a+2a+4}{\left(a-2\right)\left(a+2\right)}$$

Combine like terms in a^{2}+3-a^{2}-2a+2a+4.

$$\frac{7}{\left(a-2\right)\left(a+2\right)}$$

Expand \left(a-2\right)\left(a+2\right).

$$\frac{7}{a^{2}-4}$$