Solve 7/+2+3x/(x+2)^2-5/x

$$\frac { 7 } { + 2 } + \frac { 3 x } { ( x + 2 ) ^ { 2 } } - \frac { 5 } { x }$$

Evaluate

$$\frac{7x^{3}+24x^{2}-12x-40}{2x\left(x+2\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and \left(x+2\right)^{2} is 2\left(x+2\right)^{2}. Multiply \frac{7}{2} times \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}}. Multiply \frac{3x}{\left(x+2\right)^{2}} times \frac{2}{2}.

$$\frac{7\left(x+2\right)^{2}}{2\left(x+2\right)^{2}}+\frac{2\times 3x}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

Since \frac{7\left(x+2\right)^{2}}{2\left(x+2\right)^{2}} and \frac{2\times 3x}{2\left(x+2\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7\left(x+2\right)^{2}+2\times 3x}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

Do the multiplications in 7\left(x+2\right)^{2}+2\times 3x.

$$\frac{7x^{2}+28x+28+6x}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

Combine like terms in 7x^{2}+28x+28+6x.

$$\frac{7x^{2}+34x+28}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+2\right)^{2} and x is 2x\left(x+2\right)^{2}. Multiply \frac{7x^{2}+34x+28}{2\left(x+2\right)^{2}} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{2\left(x+2\right)^{2}}{2\left(x+2\right)^{2}}.

$$\frac{\left(7x^{2}+34x+28\right)x}{2x\left(x+2\right)^{2}}-\frac{5\times 2\left(x+2\right)^{2}}{2x\left(x+2\right)^{2}}$$

Since \frac{\left(7x^{2}+34x+28\right)x}{2x\left(x+2\right)^{2}} and \frac{5\times 2\left(x+2\right)^{2}}{2x\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(7x^{2}+34x+28\right)x-5\times 2\left(x+2\right)^{2}}{2x\left(x+2\right)^{2}}$$

Do the multiplications in \left(7x^{2}+34x+28\right)x-5\times 2\left(x+2\right)^{2}.

$$\frac{7x^{3}+34x^{2}+28x-10x^{2}-40x-40}{2x\left(x+2\right)^{2}}$$

Combine like terms in 7x^{3}+34x^{2}+28x-10x^{2}-40x-40.

$$\frac{7x^{3}+24x^{2}-12x-40}{2x\left(x+2\right)^{2}}$$

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

$$\frac{7x^{3}+24x^{2}-12x-40}{2x^{3}+8x^{2}+8x}$$

Expand

$$\frac{7x^{3}+24x^{2}-12x-40}{2x\left(x+2\right)^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and \left(x+2\right)^{2} is 2\left(x+2\right)^{2}. Multiply \frac{7}{2} times \frac{\left(x+2\right)^{2}}{\left(x+2\right)^{2}}. Multiply \frac{3x}{\left(x+2\right)^{2}} times \frac{2}{2}.

$$\frac{7\left(x+2\right)^{2}}{2\left(x+2\right)^{2}}+\frac{2\times 3x}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

Since \frac{7\left(x+2\right)^{2}}{2\left(x+2\right)^{2}} and \frac{2\times 3x}{2\left(x+2\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7\left(x+2\right)^{2}+2\times 3x}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

Do the multiplications in 7\left(x+2\right)^{2}+2\times 3x.

$$\frac{7x^{2}+28x+28+6x}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

Combine like terms in 7x^{2}+28x+28+6x.

$$\frac{7x^{2}+34x+28}{2\left(x+2\right)^{2}}-\frac{5}{x}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2\left(x+2\right)^{2} and x is 2x\left(x+2\right)^{2}. Multiply \frac{7x^{2}+34x+28}{2\left(x+2\right)^{2}} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{2\left(x+2\right)^{2}}{2\left(x+2\right)^{2}}.

$$\frac{\left(7x^{2}+34x+28\right)x}{2x\left(x+2\right)^{2}}-\frac{5\times 2\left(x+2\right)^{2}}{2x\left(x+2\right)^{2}}$$

Since \frac{\left(7x^{2}+34x+28\right)x}{2x\left(x+2\right)^{2}} and \frac{5\times 2\left(x+2\right)^{2}}{2x\left(x+2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(7x^{2}+34x+28\right)x-5\times 2\left(x+2\right)^{2}}{2x\left(x+2\right)^{2}}$$

Do the multiplications in \left(7x^{2}+34x+28\right)x-5\times 2\left(x+2\right)^{2}.

$$\frac{7x^{3}+34x^{2}+28x-10x^{2}-40x-40}{2x\left(x+2\right)^{2}}$$

Combine like terms in 7x^{3}+34x^{2}+28x-10x^{2}-40x-40.

$$\frac{7x^{3}+24x^{2}-12x-40}{2x\left(x+2\right)^{2}}$$

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

$$\frac{7x^{3}+24x^{2}-12x-40}{2x^{3}+8x^{2}+8x}$$