Solve 10/9x+10/3x^2/frac{5{3}+5/x}

$$\frac { \frac { 10 } { 9 x } + \frac { 10 } { 3 x ^ { 2 } } } { \frac { 5 } { 3 } + \frac { 5 } { x } }$$

Evaluate

$$\frac{2}{3x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x and 3x^{2} is 9x^{2}. Multiply \frac{10}{9x} times \frac{x}{x}. Multiply \frac{10}{3x^{2}} times \frac{3}{3}.

$$\frac{\frac{10x}{9x^{2}}+\frac{10\times 3}{9x^{2}}}{\frac{5}{3}+\frac{5}{x}}$$

Since \frac{10x}{9x^{2}} and \frac{10\times 3}{9x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10x+10\times 3}{9x^{2}}}{\frac{5}{3}+\frac{5}{x}}$$

Do the multiplications in 10x+10\times 3.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5}{3}+\frac{5}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x is 3x. Multiply \frac{5}{3} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{3}{3}.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5x}{3x}+\frac{5\times 3}{3x}}$$

Since \frac{5x}{3x} and \frac{5\times 3}{3x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5x+5\times 3}{3x}}$$

Do the multiplications in 5x+5\times 3.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5x+15}{3x}}$$

Divide \frac{10x+30}{9x^{2}} by \frac{5x+15}{3x} by multiplying \frac{10x+30}{9x^{2}} by the reciprocal of \frac{5x+15}{3x}.

$$\frac{\left(10x+30\right)\times 3x}{9x^{2}\left(5x+15\right)}$$

Cancel out 3x in both numerator and denominator.

$$\frac{10x+30}{3x\left(5x+15\right)}$$

Factor the expressions that are not already factored.

$$\frac{10\left(x+3\right)}{3\times 5x\left(x+3\right)}$$

Cancel out 5\left(x+3\right) in both numerator and denominator.

$$\frac{2}{3x}$$

Expand

$$\frac{2}{3x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 9x and 3x^{2} is 9x^{2}. Multiply \frac{10}{9x} times \frac{x}{x}. Multiply \frac{10}{3x^{2}} times \frac{3}{3}.

$$\frac{\frac{10x}{9x^{2}}+\frac{10\times 3}{9x^{2}}}{\frac{5}{3}+\frac{5}{x}}$$

Since \frac{10x}{9x^{2}} and \frac{10\times 3}{9x^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10x+10\times 3}{9x^{2}}}{\frac{5}{3}+\frac{5}{x}}$$

Do the multiplications in 10x+10\times 3.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5}{3}+\frac{5}{x}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and x is 3x. Multiply \frac{5}{3} times \frac{x}{x}. Multiply \frac{5}{x} times \frac{3}{3}.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5x}{3x}+\frac{5\times 3}{3x}}$$

Since \frac{5x}{3x} and \frac{5\times 3}{3x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5x+5\times 3}{3x}}$$

Do the multiplications in 5x+5\times 3.

$$\frac{\frac{10x+30}{9x^{2}}}{\frac{5x+15}{3x}}$$

Divide \frac{10x+30}{9x^{2}} by \frac{5x+15}{3x} by multiplying \frac{10x+30}{9x^{2}} by the reciprocal of \frac{5x+15}{3x}.

$$\frac{\left(10x+30\right)\times 3x}{9x^{2}\left(5x+15\right)}$$

Cancel out 3x in both numerator and denominator.

$$\frac{10x+30}{3x\left(5x+15\right)}$$

Factor the expressions that are not already factored.

$$\frac{10\left(x+3\right)}{3\times 5x\left(x+3\right)}$$

Cancel out 5\left(x+3\right) in both numerator and denominator.

$$\frac{2}{3x}$$