Solve 5/(x+2)(x-2)+6/(x+2)^2

$$\frac { 5 } { ( x + 2 ) ( x - 2 ) } + \frac { 6 } { ( x + 2 ) ^ { 2 } }$$

Evaluate

$$\frac{11x-2}{\left(x-2\right)\left(x+2\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x-2\right) and \left(x+2\right)^{2} is \left(x-2\right)\left(x+2\right)^{2}. Multiply \frac{5}{\left(x+2\right)\left(x-2\right)} times \frac{x+2}{x+2}. Multiply \frac{6}{\left(x+2\right)^{2}} times \frac{x-2}{x-2}.

$$\frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}}+\frac{6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Since \frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} and \frac{6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x+2\right)+6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Do the multiplications in 5\left(x+2\right)+6\left(x-2\right).

$$\frac{5x+10+6x-12}{\left(x-2\right)\left(x+2\right)^{2}}$$

Combine like terms in 5x+10+6x-12.

$$\frac{11x-2}{\left(x-2\right)\left(x+2\right)^{2}}$$

Expand \left(x-2\right)\left(x+2\right)^{2}.

$$\frac{11x-2}{x^{3}+2x^{2}-4x-8}$$

Expand

$$\frac{11x-2}{\left(x-2\right)\left(x+2\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x+2\right)\left(x-2\right) and \left(x+2\right)^{2} is \left(x-2\right)\left(x+2\right)^{2}. Multiply \frac{5}{\left(x+2\right)\left(x-2\right)} times \frac{x+2}{x+2}. Multiply \frac{6}{\left(x+2\right)^{2}} times \frac{x-2}{x-2}.

$$\frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}}+\frac{6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Since \frac{5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)^{2}} and \frac{6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{5\left(x+2\right)+6\left(x-2\right)}{\left(x-2\right)\left(x+2\right)^{2}}$$

Do the multiplications in 5\left(x+2\right)+6\left(x-2\right).

$$\frac{5x+10+6x-12}{\left(x-2\right)\left(x+2\right)^{2}}$$

Combine like terms in 5x+10+6x-12.

$$\frac{11x-2}{\left(x-2\right)\left(x+2\right)^{2}}$$

Expand \left(x-2\right)\left(x+2\right)^{2}.

$$\frac{11x-2}{x^{3}+2x^{2}-4x-8}$$