Solve 2/x+3/frac{4{x^2}-9}

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in 2+3x.

$$\frac{-x\left(-3x-2\right)}{\left(-3x-2\right)\left(3x-2\right)}$$

Cancel out -3x-2 in both numerator and denominator.

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

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

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

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

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

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

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

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

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

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

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

Cancel out x in both numerator and denominator.

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

Factor the expressions that are not already factored.

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

Extract the negative sign in 2+3x.

$$\frac{-x\left(-3x-2\right)}{\left(-3x-2\right)\left(3x-2\right)}$$

Cancel out -3x-2 in both numerator and denominator.

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