Solve 4/x+7/frac{16{x^2}-49}

$$\frac { \frac { 4 } { x } + 7 } { \frac { 16 } { x ^ { 2 } } - 49 }$$

Evaluate

$$-\frac{x}{7x-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{x}{x}.

$$\frac{\frac{4}{x}+\frac{7x}{x}}{\frac{16}{x^{2}}-49}$$

Since \frac{4}{x} and \frac{7x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+7x}{x}}{\frac{16}{x^{2}}-49}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 49 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{4+7x}{x}}{\frac{16}{x^{2}}-\frac{49x^{2}}{x^{2}}}$$

Since \frac{16}{x^{2}} and \frac{49x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4+7x}{x}}{\frac{16-49x^{2}}{x^{2}}}$$

Divide \frac{4+7x}{x} by \frac{16-49x^{2}}{x^{2}} by multiplying \frac{4+7x}{x} by the reciprocal of \frac{16-49x^{2}}{x^{2}}.

$$\frac{\left(4+7x\right)x^{2}}{x\left(16-49x^{2}\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(7x+4\right)}{-49x^{2}+16}$$

Factor the expressions that are not already factored.

$$\frac{x\left(7x+4\right)}{\left(-7x-4\right)\left(7x-4\right)}$$

Extract the negative sign in 4+7x.

$$\frac{-x\left(-7x-4\right)}{\left(-7x-4\right)\left(7x-4\right)}$$

Cancel out -7x-4 in both numerator and denominator.

$$\frac{-x}{7x-4}$$

Expand

$$-\frac{x}{7x-4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 7 times \frac{x}{x}.

$$\frac{\frac{4}{x}+\frac{7x}{x}}{\frac{16}{x^{2}}-49}$$

Since \frac{4}{x} and \frac{7x}{x} have the same denominator, add them by adding their numerators.

$$\frac{\frac{4+7x}{x}}{\frac{16}{x^{2}}-49}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 49 times \frac{x^{2}}{x^{2}}.

$$\frac{\frac{4+7x}{x}}{\frac{16}{x^{2}}-\frac{49x^{2}}{x^{2}}}$$

Since \frac{16}{x^{2}} and \frac{49x^{2}}{x^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4+7x}{x}}{\frac{16-49x^{2}}{x^{2}}}$$

Divide \frac{4+7x}{x} by \frac{16-49x^{2}}{x^{2}} by multiplying \frac{4+7x}{x} by the reciprocal of \frac{16-49x^{2}}{x^{2}}.

$$\frac{\left(4+7x\right)x^{2}}{x\left(16-49x^{2}\right)}$$

Cancel out x in both numerator and denominator.

$$\frac{x\left(7x+4\right)}{-49x^{2}+16}$$

Factor the expressions that are not already factored.

$$\frac{x\left(7x+4\right)}{\left(-7x-4\right)\left(7x-4\right)}$$

Extract the negative sign in 4+7x.

$$\frac{-x\left(-7x-4\right)}{\left(-7x-4\right)\left(7x-4\right)}$$

Cancel out -7x-4 in both numerator and denominator.

$$\frac{-x}{7x-4}$$