Solve 5/2x+5/9(x+2)

$$\frac { 5 } { 2 x } + \frac { 5 } { 9 ( x + 2 ) }$$

Evaluate

$$\frac{5\left(11x+18\right)}{18x\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 9\left(x+2\right) is 18x\left(x+2\right). Multiply \frac{5}{2x} times \frac{9\left(x+2\right)}{9\left(x+2\right)}. Multiply \frac{5}{9\left(x+2\right)} times \frac{2x}{2x}.

$$\frac{5\times 9\left(x+2\right)}{18x\left(x+2\right)}+\frac{5\times 2x}{18x\left(x+2\right)}$$

Since \frac{5\times 9\left(x+2\right)}{18x\left(x+2\right)} and \frac{5\times 2x}{18x\left(x+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\times 9\left(x+2\right)+5\times 2x}{18x\left(x+2\right)}$$

Do the multiplications in 5\times 9\left(x+2\right)+5\times 2x.

$$\frac{45x+90+10x}{18x\left(x+2\right)}$$

Combine like terms in 45x+90+10x.

$$\frac{55x+90}{18x\left(x+2\right)}$$

Expand 18x\left(x+2\right).

$$\frac{55x+90}{18x^{2}+36x}$$

Expand

$$\frac{5\left(11x+18\right)}{18x\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2x and 9\left(x+2\right) is 18x\left(x+2\right). Multiply \frac{5}{2x} times \frac{9\left(x+2\right)}{9\left(x+2\right)}. Multiply \frac{5}{9\left(x+2\right)} times \frac{2x}{2x}.

$$\frac{5\times 9\left(x+2\right)}{18x\left(x+2\right)}+\frac{5\times 2x}{18x\left(x+2\right)}$$

Since \frac{5\times 9\left(x+2\right)}{18x\left(x+2\right)} and \frac{5\times 2x}{18x\left(x+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{5\times 9\left(x+2\right)+5\times 2x}{18x\left(x+2\right)}$$

Do the multiplications in 5\times 9\left(x+2\right)+5\times 2x.

$$\frac{45x+90+10x}{18x\left(x+2\right)}$$

Combine like terms in 45x+90+10x.

$$\frac{55x+90}{18x\left(x+2\right)}$$

Expand 18x\left(x+2\right).

$$\frac{55x+90}{18x^{2}+36x}$$