Solve 5/x+11/frac{25{x^2}-121}

$$\frac { \frac { 5 } { x } + 11 } { \frac { 25 } { x ^ { 2 } } - 121 }$$

Evaluate

$$-\frac{x}{11x-5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{x}{x}.

$$\frac{\frac{5}{x}+\frac{11x}{x}}{\frac{25}{x^{2}}-121}$$

Since \frac{5}{x} and \frac{11x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+11x}{x}}{\frac{25}{x^{2}}-121}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 121 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{5+11x}{x}}{\frac{25}{x^{2}}-\frac{121x^{2}}{x^{2}}}$$

Since \frac{25}{x^{2}} and \frac{121x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5+11x}{x}}{\frac{25-121x^{2}}{x^{2}}}$$

Divide \frac{5+11x}{x} by \frac{25-121x^{2}}{x^{2}} by multiplying \frac{5+11x}{x} by the reciprocal of \frac{25-121x^{2}}{x^{2}}.

$$\frac{\left(5+11x\right)x^{2}}{x\left(25-121x^{2}\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(11x+5\right)}{-121x^{2}+25}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 5+11x.

$$\frac{-x\left(-11x-5\right)}{\left(-11x-5\right)\left(11x-5\right)}$$

Cancel out -11x-5 in both numerator and denominator.

$$\frac{-x}{11x-5}$$

Expand

$$-\frac{x}{11x-5}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 11 times \frac{x}{x}.

$$\frac{\frac{5}{x}+\frac{11x}{x}}{\frac{25}{x^{2}}-121}$$

Since \frac{5}{x} and \frac{11x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+11x}{x}}{\frac{25}{x^{2}}-121}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 121 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{5+11x}{x}}{\frac{25}{x^{2}}-\frac{121x^{2}}{x^{2}}}$$

Since \frac{25}{x^{2}} and \frac{121x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5+11x}{x}}{\frac{25-121x^{2}}{x^{2}}}$$

Divide \frac{5+11x}{x} by \frac{25-121x^{2}}{x^{2}} by multiplying \frac{5+11x}{x} by the reciprocal of \frac{25-121x^{2}}{x^{2}}.

$$\frac{\left(5+11x\right)x^{2}}{x\left(25-121x^{2}\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(11x+5\right)}{-121x^{2}+25}$$

Factor the expressions that are not already factored.

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

Extract the negative sign in 5+11x.

$$\frac{-x\left(-11x-5\right)}{\left(-11x-5\right)\left(11x-5\right)}$$

Cancel out -11x-5 in both numerator and denominator.

$$\frac{-x}{11x-5}$$