Solve (2/x+3/x^2)div(4/x^2-9/x)

$$( \frac { 2 } { x } + \frac { 3 } { x ^ { 2 } } ) \div ( \frac { 4 } { x ^ { 2 } } - \frac { 9 } { x } )$$

Evaluate

$$-\frac{2x+3}{9x-4}$$

Short Solution Steps

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

$$\frac{\frac{2x}{x^{2}}+\frac{3}{x^{2}}}{\frac{4}{x^{2}}-\frac{9}{x}}$$

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

$$\frac{\frac{2x+3}{x^{2}}}{\frac{4}{x^{2}}-\frac{9}{x}}$$

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

$$\frac{\frac{2x+3}{x^{2}}}{\frac{4}{x^{2}}-\frac{9x}{x^{2}}}$$

Since \frac{4}{x^{2}} and \frac{9x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2x+3}{x^{2}}}{\frac{4-9x}{x^{2}}}$$

Divide \frac{2x+3}{x^{2}} by \frac{4-9x}{x^{2}} by multiplying \frac{2x+3}{x^{2}} by the reciprocal of \frac{4-9x}{x^{2}}.

$$\frac{\left(2x+3\right)x^{2}}{x^{2}\left(4-9x\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{2x+3}{-9x+4}$$

Expand

$$\frac{2x+3}{4-9x}$$

Short Solution Steps

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

$$\frac{\frac{2x}{x^{2}}+\frac{3}{x^{2}}}{\frac{4}{x^{2}}-\frac{9}{x}}$$

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

$$\frac{\frac{2x+3}{x^{2}}}{\frac{4}{x^{2}}-\frac{9}{x}}$$

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

$$\frac{\frac{2x+3}{x^{2}}}{\frac{4}{x^{2}}-\frac{9x}{x^{2}}}$$

Since \frac{4}{x^{2}} and \frac{9x}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2x+3}{x^{2}}}{\frac{4-9x}{x^{2}}}$$

Divide \frac{2x+3}{x^{2}} by \frac{4-9x}{x^{2}} by multiplying \frac{2x+3}{x^{2}} by the reciprocal of \frac{4-9x}{x^{2}}.

$$\frac{\left(2x+3\right)x^{2}}{x^{2}\left(4-9x\right)}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{2x+3}{-9x+4}$$