Solve 7/9x^2+x/3x^2+3x

$$\frac { 7 } { 9 x ^ { 2 } } + \frac { x } { 3 x ^ { 2 } + 3 x }$$

Evaluate

$$\frac{3x^{2}+7x+7}{9\left(x+1\right)x^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x}{3x^{2}+3x}.

$$\frac{7}{9x^{2}}+\frac{x}{3x\left(x+1\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{7}{9x^{2}}+\frac{1}{3\left(x+1\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x^{2} and 3\left(x+1\right) is 9\left(x+1\right)x^{2}. Multiply \frac{7}{9x^{2}} times \frac{x+1}{x+1}. Multiply \frac{1}{3\left(x+1\right)} times \frac{3x^{2}}{3x^{2}}.

$$\frac{7\left(x+1\right)}{9\left(x+1\right)x^{2}}+\frac{3x^{2}}{9\left(x+1\right)x^{2}}$$

Since \frac{7\left(x+1\right)}{9\left(x+1\right)x^{2}} and \frac{3x^{2}}{9\left(x+1\right)x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{7\left(x+1\right)+3x^{2}}{9\left(x+1\right)x^{2}}$$

Do the multiplications in 7\left(x+1\right)+3x^{2}.

$$\frac{7x+7+3x^{2}}{9\left(x+1\right)x^{2}}$$

Expand 9\left(x+1\right)x^{2}.

$$\frac{7x+7+3x^{2}}{9x^{3}+9x^{2}}$$

Factor

$$\frac{3x^{2}+7x+7}{9\left(x+1\right)x^{2}}$$